Complex multiplication and lifting problems / Ching-Li Chai, Brian Conrad and Frans Oort.
Material type:
TextSeries: Mathematical surveys and monographs ; v 195.Publication details: Providence : American Mathematical Society, c2014.Description: ix, 387 p. : ill. ; 26 cmISBN: - 9781470410148 (alk. paper)
- 510MS 23 Am512
| Item type | Current library | Call number | Status | Date due | Barcode | Item holds | |
|---|---|---|---|---|---|---|---|
| Books | ISI Library, Kolkata | 510MS Am512 (Browse shelf(Opens below)) | Available | 135865 |
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| 510MS Am512 An introduction to central simple algebras and their applications to wireless communication / | 510MS Am512 Attractors for degenerate parabolic type equations / | 510MS Am512 Stochastic resonance : | 510MS Am512 Complex multiplication and lifting problems / | 510MS Am512 Geometry of isotropic convex bodies / | 510MS Am512 Octogonal PETs / | 510MS Am512 Brauer groups, tamagawa measures, and rational points on algebraic varieties / |
Includes bibliographical references (pages 379-383) and index.
Preface --
Introduction --
References --
Notation and terminology -
1. Algebraic Theory of Complex Multiplication --
2. CM lifting over a discrete valuation ring --
3. CM lifting of p-divisible groups --
4. CM Lifting of abelian varieties up to isogeny --
Appendix A: Some arithmetic results for abelian varieties --
Appendix B. CM lifting via p-adic Hodge theory --
Notes on Quotes --
Glossary of Notations --
Bibliography --
Index.
This book explores the relationship between such abelian varieties over finite fields and over arithmetically interesting fields of characteristic 0 via the study of several natural CM lifting problems which had previously been solved only in special cases. In addition to giving complete solutions to such questions, the authors provide numerous examples to illustrate the general theory and present a detailed treatment of many fundamental results and concepts in the arithmetic of abelian varieties, such as the Main Theorem of Complex Multiplication and its generalizations, the finer aspects of Tate's work on abelian varieties over finite fields, and deformation theory. This book provides an ideal illustration of how modern techniques in arithmetic geometry (such as descent theory, crystalline methods, and group schemes) can be fruitfully combined with class field theory to answer concrete questions about abelian varieties. It will be a useful reference for researchers and advanced graduate students at the interface of number theory and algebraic geometry. -- Provided by publisher.
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