rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Complex multiplication and lifting problems
  name:
    name part: Chai, Ching-Li
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Conrad, Brian
    name part: 1970-
    role:
      role term: author.
  name:
    name part: Oort, Frans
    name part: 1935-
    role:
      role term: author.
  type of resource: text
  genre: bibliography
  origin info:
    place:
      place term: riu
    date issued: 2014
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: print
    extent: ix, 387 pages ; 26 cm.
  abstract: Abelian 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.
  note: Ching-Li Chai, Brian Conrad, Frans Oort.
  note: Includes bibliographical references (pages 379-383) and index.
  subject:
    topic: Multiplication, Complex
  subject:
    topic: Abelian varieties
  subject:
    topic: Lifting theory
  subject:
    topic: Number theory -- Arithmetic algebraic geometry (Diophantine geometry) -- Complex multiplication and moduli of abelian varieties
  subject:
    topic: Algebraic geometry -- Abelian varieties and schemes -- Isogeny
  subject:
    topic: Algebraic geometry -- Algebraic groups -- Formal groups, $p$-divisible groups
  subject:
    topic: Algebraic geometry -- Abelian varieties and schemes -- Arithmetic ground fields
  subject:
    topic: Algebraic geometry -- Families, fibrations -- Formal methods; deformations
  classification: QA564 .C44 2014
  classification: 516.3/53
  classification: 11G15 14K02 14L05 14K15 14D15
  related item:
    title info:
      title: Mathematical surveys and monographs ; no. 195
  identifier: 9781470410148 (alk. paper)
  identifier: 1470410141 (alk. paper)
  identifier: 2013036892
  record info:
    record content source: DLC
    record creation date: 130912
    record change date: 20151206091940.0
    record identifier: in00003429925
    language of cataloging:
      language term: eng