Barsotti Symposium in Algebraic Geometry (eBook)

Valentino Cristante, William Messing (Herausgeber)

eBook Download: PDF

2014 | 1. Auflage
304 Seiten
Elsevier Science (Verlag)
978-1-4832-1762-8 (ISBN)

Infos

Barsotti Symposium in Algebraic Geometry contains papers corresponding to the lectures given at the 1991 memorial meeting held in Abano Terme in honor of Iacopo Barsotti. This text reflects Barsotti's significant contributions in the field. This book is composed of 10 chapters and begins with a review of the centers of three-dimensional skylanin algebras. The succeeding chapters deal with the theoretical aspects of the Abelian varieties, Witt realization of p-Adic Barsotti-Tate Groups, and hypergeometric series and functions. These topics are followed by discussions of logarithmic spaces and the estimates for and inequalities among A-numbers. The closing chapter describes the moduli of Abelian varieties in positive characteristic. This book will be of value to mathematicians.

Inhalt

Front Cover 1
Barsotti Symposium in Algebraic Geometry 4
Copyright Page 5
Table of Contents 6
Contributors 8
Introduction 10
Biographical Notices about Iacopo BARSOTTI 15
Barsotti's Publications 16
Chapter 1. The Centers of 3-Dimensional Sklyanin Algebras 18
REFERENCES 27
Chapter 2. Algebraic versis Rigid Cohomology with Logarithmic Coefficients 28
§1 Notation 28
§2 Main Result 29
§3 The 1-dimensional example: role of hypotheses (NL)G and (SC)G 34
§4 Existence of tubular neighborhoods of radius 1 of .k in Yk 42
§5 Systems with logarithmic singularities on relative open polydisks of radius 1. ([Ba-Ct2]) 46
§6 Local comparison theorem 56
References 66
Chapter 3. Abelian Varieties from the Rigid Analytic Viewpoint 68
1 Uniformization of Abelian Varieties 69
2 The Theory of Raynaud Extensions and their Duals 73
3 Polarizations 77
References 79
Chapter 4. Witt Realization of p-Adic Barsotti-Tate Groups 82
Introduction 82
0. Notations 84
1. Immersion of étale BT-groups 97
2. Extensions of B-T groups over k with Witt groups 101
3. Extensions of local A-groups by étale A-groups 113
4 Rigidified extensions associated to liftings of a BT-group over k 116
5. Sub-A'-modules of .' Ä M(R) and liftings of BT-groups 127
REFERENCES 139
Chapter 5. A p-Adic Inner Product on Elliptic Modular Forms 142
Notation 143
1. The inner product 144
2. Ordinary forms and the Serre-Tate invariant 149
3. Integral Structures 150
4. Integrality 154
5. Reduction 157
Appendix 161
References 168
Chapter 6. Hypergeometric Series and Functions as Periods of Exponential Modules 170
§1. Exponential Module 170
§2. Dual space 172
§3. Proof of Theorem A 173
§4. Periods of exponential modules 176
§5. Application 177
§6. Hypersurfaces 179
§7. Modified hypergeometric series 182
§8. Delsarte Sums 182
§9. New Method 184
Bibliography 191
Chapter 7. The General Case of S. Lang's Conjecture 192
1. INTRODUCTION 192
2. SOME NUMERICS 193
3. ABRAMOVICH'S METHOD 194
5. COMPLEMENTS 198
REFERENCES 199
Chapter 8. Logarithmic Spaces (According to K. Kato) 200
0. Introduction 200
1. Logarithmic structures 202
2. Log crystalline cohomology 207
3. Log degeneration of commutative group schemes 211
REFERENCES 218
Chapter 9. Perversity and Exponential Sums II: Estimates for and Inequalities among A-Numbers 222
INTRODUCTION 222
1. GENERALITIES ON A-NUMBERS 224
2. LOCAL COMPLETE INTERSECTIONS 229
3. DlOPHANTINE CALCULATIONS VIA PROJECTIVE VARIETIES 230
4. THE CASE OF ISOLATED SINGULARITIES 234
5. DETAILED STUDY OF HYPERSURFACES WITH ISOLATED SINGULARITIES 235
6. HYPERSURFACES WITH ORDINARY DOUBLE POINTS 236
7. A-NUMBERS INEQUALITIES 241
8. BEGINNING OF THE PROOF OF THEOREM 7.1 243
9. PROOF OF INEQUALITY (1) OF 7.1 250
10. INTERLUDE: WEIGHTS AND LOCAL MONODROMY 251
11. THE A-NUMBER OF f(x) = g(y) 252
12. THE A-NUMBER OF y1y2...ys = ß VIA KLOOSTERMAN SHEAVES 254
13. PROOF OF INEQUALITIES (2) AND (3) OF 7.1 257
14. VARIANTS OF THE THIRD INEQUALITY 264
15. SOME EXACT FORMULAS FOR A-NUMBERS 265
REFERENCES 269
Chapter 10. Moduli of Abelian Varieties in Positive Characteristic 270
Introduction 270
1. Definitions and prerequisites 271
2. The Vi are connected 278
3. The stratification by Newton polygons 281
4. Supersingular abelian varieties 285
References 289
Index 294
Perspectives in Mathematics 306

Produkt-Details

• Erscheint lt. Verlag: 21.7.2014
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Themenwelt: Technik
• ISBN-10: 1-4832-1762-0 / 1483217620
• ISBN-13: 978-1-4832-1762-8 / 9781483217628