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: P-Adic Automorphic Forms on Shimura Varieties
  name:
    name part: Hida, Haruzo.
    role:
      role term: creator
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  genre: Electronic books.
  origin info:
    place:
      place term: nyu
    date issued: 2004
    issuance: monographic
  language:
    language term: eng
  physical description:
    reformatting quality: access
    form: remote
    extent: 1 online resource (xi, 390 pages)
  abstract: This book covers the following three topics in a manner accessible to graduate students who have an understanding of algebraic number theory and scheme theoretic algebraic geometry: 1. An elementary construction of Shimura varieties as moduli of abelian schemes. 2. p-adic deformation theory of automorphic forms on Shimura varieties. 3. A simple proof of irreducibility of the generalized Igusa tower over the Shimura variety. The book starts with a detailed study of elliptic and Hilbert modular forms and reaches to the forefront of research of Shimura varieties associated with general classical groups. The method of constructing p-adic analytic families and the proof of irreducibility was recently discovered by the author. The area covered in this book is now a focal point of research worldwide with many far-reaching applications that have led to solutions of longstanding problems and conjectures. Specifically, the use of p-adic elliptic and Hilbert modular forms have proven essential in recent breakthroughs in number theory (for example, the proof of Fermat's Last Theorem and the Shimura-Taniyama conjecture by A. Wiles and others). Haruzo Hida is Professor of Mathematics at University of California, Los Angeles. His previous books include Modular Forms and Galois Cohomology (Cambridge University Press 2000) and Geometric Modular Forms and Elliptic Curves (World Scientific Publishing Company 2000).
  table of contents: Introduction -- Geometric Reciprocity Laws -- Modular Curves -- Hilbert Modular Varieties -- Generalized Eichler-Shimura Map -- Moduli Schemes -- Shimura Varieties -- p-Adic Automorphic Forms -- Bibliography.
  note: by Haruzo Hida.
  note: Electronic resource.
  subject:
    topic: Mathematics
  subject:
    topic: Geometry, Algebraic
  subject:
    topic: Number theory
  subject:
    topic: Geometry, Algebraic
  subject:
    topic: Mathematics
  subject:
    topic: Number theory
  classification: QA241-247.5
  classification: 512.7
  related item:
    title info:
      title: Springer monographs in mathematics
  identifier: 9781468493900 (electronic bk.)
  identifier: 1468493906 (electronic bk.)
  identifier: 9781441919236
  identifier: 1441919236
  identifier: 1468493906
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: AU@
    record creation date: 121227
    record change date: 20260422202955.2
    record identifier: in00003570719
    language of cataloging:
      language term: eng