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Front matter
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Index
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Front matter
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Issue 1-2: L'ENSEIGNEMENT MATHÉMATIQUE
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1
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Article
THE SCHUR SUBGROUP OF THE BRAUER GROUP OF A LOCAL FIELD
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1
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Chapter
K NON-DYADIC
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2
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Chapter
Remarks
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9
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Bibliography
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10
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Article
UNE CARACTÉRISATION DES NORMES EUCLIDIENNES EN DIMENSION FINIE
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13
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Chapter
Introduction
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13
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Chapter
I. Groupe des isométries linéaires
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14
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Chapter
II. La boule unité de L(E)
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15
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Chapter
III. Application au cas n = 2
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18
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Bibliography
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21
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Article
EULER'S FAMOUS PRIME GENERATING POLYNOMIAL AND THE CLASS NUMBER OF IMAGINARY QUADRATIC FIELDS
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23
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Chapter
Introduction
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23
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Chapter
A) Quadratic extensions
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25
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Chapter
B) Rings of integers
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26
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Chapter
C) Discriminant
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27
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Chapter
D) Decomposition of primes
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27
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Chapter
E) Units
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32
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Chapter
F) The class number
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33
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Chapter
G) The main theorem
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40
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Bibliography
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42
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Article
LE PROBLÈME DE GAUSS SUR LE NOMBRE DE CLASSES
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43
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Chapter
I. La classification de Gauss des formes quadratiques
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44
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Chapter
§1. FINITUDE DU NOMBRE DE CLASSES
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44
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Chapter
§2. Formes quadratiques réduites
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45
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Chapter
§3. Une méthode élémentaire pour calculer le nombre de classes
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47
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Chapter
§4. Le groupe des classes
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48
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Chapter
§5. Lien entre h(-d) et $h(-df^2)$
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51
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Chapter
II. Le problème du nombre de classes
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52
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Chapter
§1. Représentation des entiers par les formes quadratiques
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53
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Chapter
§2. Fonctions zêta
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55
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Chapter
§3. Ce que l'on espère sur le comportement de h( —d)
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57
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Chapter
§4. Minorations non effectives de h(—d)
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59
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Chapter
§5. Les cas h = 1 et h = 2
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60
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Chapter
§6. Courbes elliptiques et fonctions L
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61
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Chapter
§7. Le théorème de Goldfeld
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64
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Chapter
§8. Le théorème de Gross et Zagier
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65
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Chapter
§9. Conclusion
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66
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Article
ON TORRES-TYPE RELATIONS FOR THE ALEXANDER POLYNOMIALS OF LINKS
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69
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Chapter
§1. Introduction
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69
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Chapter
§2. Torsions of chain complexes and manifolds
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72
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Chapter
§3. Algebraic lemmas
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74
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Chapter
§4. Proof of Theorems 1 and 2
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76
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Bibliography
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82
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Article
EXTENSIONS DE MODULES ET COHOMOLOGIE DES GROUPES
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83
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Chapter
Introduction
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83
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Chapter
1. Rappels sur les extensions
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83
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Chapter
2. DÉRIVATIONS ET EXTENSIONS
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85
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Chapter
3. Le groupe $H^1(G;A)$
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87
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Chapter
4. Le groupe $H^2(G;A)$
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93
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Article
ABOUT THE PROOFS OF CALABI'S CONJECTURES ON COMPACT KÄHLER MANIFOLDS
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107
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Abstract
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107
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Chapter
0. Introduction
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107
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Chapter
1. The Monge-Ampère equation
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108
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Chapter
2. A Topological Lemma
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110
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Chapter
3. Local inversion
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111
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Chapter
4. Properness
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111
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Chapter
5. A PRIORI ESTIMATES: THE ORIGINAL WAY
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114
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Chapter
6. Coordinate free tensor calculus
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114
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Chapter
7. HIGHER ORDER A PRIORI ESTIMATES: GENERALITIES
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115
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Chapter
8. A PRIORI ESTIMATES OF ORDER FOUR
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118
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Chapter
9. A PRIORI ESTIMATES OF ORDER FIVE AND MORE
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120
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Chapter
10. The analytic point of view
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121
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Bibliography
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121
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Article
QUILLEN'S THEOREM ON BUILDINGS AND THE LOOPS ON A SYMMETRIC SPACE
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123
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Abstract
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123
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Chapter
§1. Notation and Preliminaries
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128
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Chapter
§2. Topological Buildings
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134
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Chapter
§3. Loop Groups
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142
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Chapter
§4. Quillen's Theorem for Loop Groups
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144
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Chapter
§5. The Loops on a Symmetric Space
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147
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Chapter
§6. Examples
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152
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Chapter
§7. Bott Periodicity
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158
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Appendix
§8. Appendix : Real Forms and the generalized bruhat decomposition
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161
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Bibliography
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165
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Article
ISOCLINIC n-PLANES IN $R^{2n}$ AND THE HOPF-STEENROD SPHERE BUNDLES $S^{2n-1} \rightarrow S^n,\quad n=2,4,8$
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167
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Chapter
0. Introduction
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167
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Chapter
1. Some results on isoclinic n-PLANES in $R^{2n}$
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168
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Chapter
2. SOME FURTHER RESULTS
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173
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Chapter
3. The sphère bundles $S^{2n-1} \rightarrow \Phi_n, \quad n=2,4,or 8$, WITH FIBERS ON MUTUALLY ISOCLINIC n-PLANES IN $R^{2n}$
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181
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Chapter
4. A UNIFIED TREATMENT OF THE THREE HOPF-STEENROD BUNDLES
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187
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Chapter
5. COMPARISON OF OUR BUNDLES WITH THE HOPF-STEENROD BUNDLES
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194
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Appendix
Appendix 1. The Cayley numbers
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200
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Appendix
Appendix 2. The Hopf fibering and mutually isoclinic planes
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201
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Bibliography
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204
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Rubric
COMMISSION INTERNATIONALE DE L'ENSEIGNEMENT MATHÉMATIQUE (THE INTERNATIONAL COMMISSION ON MATHEMATICAL INSTRUCTION)
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205
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Article
THE POPULARIZATION OF MATHEMATICS
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205
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Chapter
1. A GENERAL FRAMEWORK: NEEDS AND METHODS FOR THE POPULARIZATION OF SCIENCE
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206
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Chapter
2. Spécial features of the popularization of mathematics
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207
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Chapter
3. The methods of popularization
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210
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Chapter
Call for papers
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212
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Chapter
Previous ICMI Studies
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213
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Article
THE THEORY OF GRÖBNER BASES
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215
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Chapter
Introduction
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215
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Chapter
1. Notations and Definitions
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216
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Chapter
2. The Division Algorithm
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220
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Chapter
3. Construction of Gröbner Bases
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223
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Chapter
4. Application to Systems of Algebraic Equations
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228
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Chapter
5. Application to a Geometric Problem
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230
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Bibliography
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231
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Article
GEODESICS IN THE UNIT TANGENT BUNDLE OF A ROUND SPHERE
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233
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Chapter
1. Geometry of the unit tangent bundle
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235
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Chapter
2. Geodesics in $US^2$
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238
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Chapter
3. Helices in $S^3$
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239
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Chapter
4. SASAKI'S EQUATIONS
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240
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Chapter
5. Proof of the Fundamental Constraint
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243
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Bibliography
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246
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Article
THE EULER CLASS OF ORTHOGONAL RATIONAL REPRESENTATIONS OF FINITE GROUPS
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247
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Chapter
1. Invariant Bilinear Forms
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248
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Chapter
2. Orthogonal representations of p-groups
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249
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Chapter
3. Proof of the main theorem
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252
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Bibliography
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253
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Article
UNE THÉORIE DE DENJOY DES MARTINGALES DYADIQUES
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255
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Chapter
problème
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255
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Chapter
solution: totalisation dyadique
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257
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Chapter
Commentaires
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261
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Appendix
Appendice: distribution de la fonction f
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263
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Chapter
CITATIONS ET PASTICHE
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266
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Bibliography
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268
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Article
AN ELEMENTARY PROOF OF THE STRUCTURE THEOREM FOR CONNECTED SOLVABLE AFFINE ALGEBRAIC GROUPS
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269
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Abstract
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269
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Rubric
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270
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Bibliography
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273
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Article
KALUZA-KLEIN APPROACH TO HYPERBOLIC THREE-MANIFOLDS
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275
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Chapter
§1. Introduction
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275
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Chapter
§2. CONFORMAL COMPACTIFICATIONS AND THEIR TOPOLOGY
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277
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Chapter
§3. Classification of Γ with $dim_H\Lambda(\Gamma)\leq 1$
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284
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Chapter
§4. HODGE THEORY FOR HYPERBOLIC 3-MANIFOLDS
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287
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Chapter
§5. Monopoles and Instantons
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291
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Chapter
§6. Twistor spaces
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295
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Chapter
§7. Atiyah-Ward ansatzes, summing 't Hooft solutions and elsenstein series
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305
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Bibliography
|
310
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Article
SOME ALMOST HOMOGENEOUS GROUP ACTIONS ON SMOOTH COMPLETE RATIONAL SURFACES
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313
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Chapter
§1. Minimal embeddings: définitions and preliminary remarks
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314
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Chapter
§2. The minimal B/Γ-embeddings
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317
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Chapter
§3. Application to SL(2)-embeddings
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331
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Bibliography
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332
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Article
REPRÉSENTATIONS ET TRACES DES ALGÈBRES DE HECKE POLYNÔME DE JONES-CONWAY
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333
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Chapter
§0. Introduction
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333
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Chapter
§1. Une description du polynôme de Jones-Conway
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336
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Chapter
§2. Représentations des algèbres de Hecke
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340
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Chapter
§3. Traces des algèbres de Hecke
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342
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Chapter
§4. La trace T
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345
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Chapter
§5. La trace de Jones-Ocneanu
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348
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Chapter
§6. Une généralisation du polynôme de Jones-Conway
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349
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Bibliography
|
355
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Article
GLOBAL CONSTRUCTION OF THE NORMALIZATION OF STEIN SPACES
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357
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Chapter
Introduction
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357
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Chapter
1. Example of a Stein space X with $\widetilde{O(X)} \neq O(\tilde{X})$
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358
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Chapter
2. Construction of $O(\tilde{X})$ from O(X) for Stein spaces X
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360
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Chapter
3. Applications
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361
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Bibliography
|
363
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Article
LES ÉQUATIONS DIFFÉRENTIELLES ONT 350 ANS
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365
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Chapter
problèmes de Debeaune
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365
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Chapter
«Discorsi» de Galilée
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366
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Chapter
Newton
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367
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Chapter
Solution du premier problème de Debeaune
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369
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Chapter
problème de l'isochrone
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370
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Chapter
caténaire
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371
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Chapter
tractrice
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373
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Chapter
L'ÉQUATION DIFFÉRENTIELLE «DE BERNOULLI»
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374
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Chapter
Brachystochrone
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375
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Chapter
PROBLÈMES ISOPÉRIMÉTRIQUES
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377
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Chapter
Euler et Lagrange
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379
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Chapter
Problèmes isopérimétriques, suite
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380
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Chapter
Epilogue
|
381
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Chapter
Exercices
|
382
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Bibliography
|
384
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Article
LES GRANDS THÈMES DE FRANÇOIS CHÂTELET
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387
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Chapter
1. Variétés de Severi-Brauer
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387
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Chapter
1.1. Avant Châtelet.
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387
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Chapter
1.2. La contribution de F. Châtelet [1943a] [1943b] [1944].
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389
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Chapter
1.3. Après les travaux de Châtelet.
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391
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Chapter
1.4. Importance des variétés de Severi-Brauer.
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391
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Chapter
2. Courbes de genre 1
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392
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Chapter
2.1. Avant Châtelet.
|
392
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Chapter
2.2. La contribution de Châtelet [1938] [1941] [1946a] [1947a].
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393
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Chapter
2.3. Après Châtelet.
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395
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Chapter
2.4. Points de torsion.
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395
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Chapter
3. Surfaces cubiques
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396
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Chapter
3.1. Avant Châtelet.
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396
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Chapter
3.2. La contribution de Châtelet [1953] [1954 a] [1954b] [1958] [1959b] [1966].
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397
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Chapter
3.3. Après Châtelet.
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399
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Chapter
ARTICLES DE FRANÇOIS CHÂTELET
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401
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Bibliography
|
403
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Rubric
BULLETIN BIBLIOGRAPHIQUE
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1
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Rubric
BULLETIN BIBLIOGRAPHIQUE
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41
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Back matter
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