000 02428cam a2200277 i 4500
001 135865
003 ISI Library, Kolkata
005 20150617114230.0
008 130912s2014 riu b 001 0 eng
020 _a9781470410148 (alk. paper)
040 _aISI Library
082 0 0 _a510MS
_223
_bAm512
100 1 _aChai, Ching-Li.
245 1 0 _aComplex multiplication and lifting problems /
_cChing-Li Chai, Brian Conrad and Frans Oort.
260 _aProvidence :
_bAmerican Mathematical Society,
_cc2014.
300 _aix, 387 p. :
_bill. ;
_c26 cm.
490 0 _aMathematical surveys and monographs ;
_vv 195.
504 _aIncludes bibliographical references (pages 379-383) and index.
505 0 _aPreface -- 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.
520 _aThis 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.
650 0 _aComplex Multiplication.
650 0 _aAbelian varieties.
700 1 _aConrad, Brian.
700 1 _aOort, Frans.
942 _2ddc
_cBK
999 _c418751
_d418751