Cristante / Messing Barsotti Symposium in Algebraic Geometry

1. Auflage 2014
ISBN: 978-1-4832-1762-8
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band Volume 15, 304 Seiten, Web PDF

Reihe: Perspectives in Mathematics

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.

Autoren/Hrsg.

Cristante, Valentino

Messing, William

Inhaltsverzeichnis

1;Front Cover;1
2;Barsotti Symposium in Algebraic Geometry;4
3;Copyright Page;5
4;Table of Contents;6
5;Contributors;8
6;Introduction;10
7;Biographical Notices about Iacopo BARSOTTI;15
8;Barsotti's Publications;16
9;Chapter 1. The Centers of 3-Dimensional Sklyanin Algebras;18
9.1;REFERENCES;27
10;Chapter 2. Algebraic versis Rigid Cohomology with Logarithmic Coefficients;28
10.1;§1 Notation;28
10.2;§2 Main Result;29
10.3;§3 The 1-dimensional example: role of hypotheses (NL)G and (SC)G;34
10.4;§4 Existence of tubular neighborhoods of radius 1 of .k in Yk;42
10.5;§5 Systems with logarithmic singularities on relative open polydisks of radius 1. ([Ba-Ct2]);46
10.6;§6 Local comparison theorem;56
10.7;References;66
11;Chapter 3. Abelian Varieties from the Rigid Analytic Viewpoint;68
11.1;1 Uniformization of Abelian Varieties;69
11.2;2 The Theory of Raynaud Extensions and their Duals;73
11.3;3 Polarizations;77
11.4;References;79
12;Chapter 4. Witt Realization of p-Adic Barsotti-Tate Groups;82
12.1;Introduction;82
12.2;0. Notations;84
12.3;1. Immersion of étale BT-groups;97
12.4;2. Extensions of B-T groups over k with Witt groups;101
12.5;3. Extensions of local A-groups by étale A-groups;113
12.6;4 Rigidified extensions associated to liftings of a BT-group over k;116
12.7;5. Sub-A'-modules of .' Ä M(R) and liftings of BT-groups;127
12.8;REFERENCES;139
13;Chapter 5. A p-Adic Inner Product on Elliptic Modular Forms;142
13.1;Notation;143
13.2;1. The inner product;144
13.3;2. Ordinary forms and the Serre-Tate invariant;149
13.4;3. Integral Structures;150
13.5;4. Integrality;154
13.6;5. Reduction;157
13.7;Appendix;161
13.8;References;168
14;Chapter 6. Hypergeometric Series and Functions as Periods of Exponential Modules;170
14.1;§1. Exponential Module;170
14.2;§2. Dual space;172
14.3;§3. Proof of Theorem A;173
14.4;§4. Periods of exponential modules;176
14.5;§5. Application;177
14.6;§6. Hypersurfaces;179
14.7;§7. Modified hypergeometric series;182
14.8;§8. Delsarte Sums;182
14.9;§9. New Method;184
14.10;Bibliography;191
15;Chapter 7. The General Case of S. Lang's Conjecture;192
15.1;1. INTRODUCTION;192
15.2;2. SOME NUMERICS;193
15.3;3. ABRAMOVICH'S METHOD;194
15.4;5. COMPLEMENTS;198
15.5;REFERENCES;199
16;Chapter 8. Logarithmic Spaces (According to K. Kato);200
16.1;0. Introduction;200
16.2;1. Logarithmic structures;202
16.3;2. Log crystalline cohomology;207
16.4;3. Log degeneration of commutative group schemes;211
16.5;REFERENCES;218
17;Chapter 9. Perversity and Exponential Sums II: Estimates for and Inequalities among A-Numbers;222
17.1;INTRODUCTION;222
17.2;1. GENERALITIES ON A-NUMBERS;224
17.3;2. LOCAL COMPLETE INTERSECTIONS;229
17.4;3. DlOPHANTINE CALCULATIONS VIA PROJECTIVE VARIETIES;230
17.5;4. THE CASE OF ISOLATED SINGULARITIES;234
17.6;5. DETAILED STUDY OF HYPERSURFACES WITH ISOLATED SINGULARITIES;235
17.7;6. HYPERSURFACES WITH ORDINARY DOUBLE POINTS;236
17.8;7. A-NUMBERS INEQUALITIES;241
17.9;8. BEGINNING OF THE PROOF OF THEOREM 7.1;243
17.10;9. PROOF OF INEQUALITY (1) OF 7.1;250
17.11;10. INTERLUDE: WEIGHTS AND LOCAL MONODROMY;251
17.12;11. THE A-NUMBER OF f(x) = g(y);252
17.13;12. THE A-NUMBER OF y1y2...ys = ß VIA KLOOSTERMAN SHEAVES;254
17.14;13. PROOF OF INEQUALITIES (2) AND (3) OF 7.1;257
17.15;14. VARIANTS OF THE THIRD INEQUALITY;264
17.16;15. SOME EXACT FORMULAS FOR A-NUMBERS;265
17.17;REFERENCES;269
18;Chapter 10. Moduli of Abelian Varieties in Positive Characteristic;270
18.1;Introduction;270
18.2;1. Definitions and prerequisites;271
18.3;2. The Vi are connected;278
18.4;3. The stratification by Newton polygons;281
18.5;4. Supersingular abelian varieties;285
18.6;References;289
19;Index;294
20;Perspectives in Mathematics;306