MARC Record from harvard_bibliographic_metadata

LEADER: 03625cam a2200469 i 4500
001 013906202-5
005 20140117131258.0
008 130912s2014 riua b 001 0 eng
010 $a 2013036892
020 $a9781470410148 (alk. paper)
020 $a1470410141 (alk. paper)
035 0 $aocn858778275
040 $aDLC$erda$beng$cDLC$dYDX$dOCLCO$dBTCTA$dYDXCP$dORC$dOCLCO
042 $apcc
050 00 $aQA564$b.C44 2014
082 00 $a516.3/53$223
084 $a11G15$a14K02$a14L05$a14K15$a14D15$2msc
100 1 $aChai, Ching-Li,$eauthor.
245 10 $aComplex multiplication and lifting problems /$cChing-Li Chai, Brian Conrad, Frans Oort.
264 1 $aProvidence, Rhode Island :$bAmerican Mathematical Society,$c[2014]
300 $aix, 387 pages ;$c26 cm.
336 $atext$2rdacontent
337 $aunmediated$2rdamedia
338 $avolume$2rdacarrier
490 1 $aMathematical surveys and monographs ;$vvolume 195
504 $aIncludes bibliographical references and index.
505 0 $aPreface -- Introduction -- References -- Notation and terminology - Algebraic Theory of Complex Multiplication -- CM lifting over a discrete valuation ring -- CM lifting of p-divisible groups -- CM Lifting of abelian varieties up to isogeny -- Appendix A: Some arithmetic results for abelian varieties -- CM lifting via p-adic Hodge theory -- Notes on Quotes -- Glossary of Notations -- Bibliography -- Index
520 $aAbelian varieties with complex multiplication lie at the origins of class field theory, and they play a central role in the contemporary theory of Shimura varieties. They are special in characteristic 0 and ubiquitous over finite fields. 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.
650 0 $aMultiplication, Complex.
650 0 $aAbelian varieties.
650 7 $aNumber theory -- Arithmetic algebraic geometry (Diophantine geometry) -- Complex multiplication and moduli of abelian varieties.$2msc
650 7 $aAlgebraic geometry -- Abelian varieties and schemes -- Isogeny.$2msc
650 7 $aAlgebraic geometry -- Algebraic groups -- Formal groups, $p$-divisible groups.$2msc
650 7 $aAlgebraic geometry -- Abelian varieties and schemes -- Arithmetic ground fields.$2msc
650 7 $aAlgebraic geometry -- Families, fibrations -- Formal methods; deformations.$2msc
650 0 $aLifting theory.
700 1 $aConrad, Brian,$d1970-$eauthor.
700 1 $aOort, Frans,$d1935-$eauthor.
830 0 $aMathematical surveys and monographs ;$vno. 195.
988 $a20140117
049 $aCLSL
906 $0DLC