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: Elliptic curves
  name:
    name part: Husemöller, Dale.
    role:
      role term: creator
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  genre: bibliography
  genre: Electronic books.
  origin info:
    place:
      place term: nyu
    date issued: 2004
    edition: 2nd ed.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: remote
    extent: 1 online resource (xxi, 487 pages) : illustrations.
  abstract: This book is an introduction to the theory of elliptic curves, ranging from elementary topics to current research. The first chapters, which grew out of Tate's Haverford Lectures, cover the arithmetic theory of elliptic curves over the field of rational numbers. This theory is then recast into the powerful and more general language of Galois cohomology and descent theory. An analytic section of the book includes such topics as elliptic functions, theta functions, and modular functions. Next, the book discusses the theory of elliptic curves over finite and local fields and provides a survey of results in the global arithmetic theory, especially those related to the conjecture of Birch and Swinnerton-Dyer. This new edition contains three new chapters. The first is an outline of Wiles's proof of Fermat's Last Theorem. The two additional chapters concern higher-dimensional analogues of elliptic curves, including K3 surfaces and Calabi-Yau manifolds. Two new appendices explore recent applications of elliptic curves and their generalizations. The first, written by Stefan Theisen, examines the role of Calabi-Yau manifolds and elliptic curves in string theory, while the second, by Otto Forster, discusses the use of elliptic curves in computing theory and coding theory. About the First Edition: "All in all the book is well written, and can serve as basis for a student seminar on the subject."--G. Faltings, Zentralblatt.
  table of contents: Introduction to Rational Points on Plane Curves -- Elementary Properties of the Chord-Tangent Group Law on a Cubic Curve -- Plane Algebraic Curves -- Factorial Rings and Elimination Theory -- Elliptic Curves and Their Isomorphism -- Families of Elliptic Curves and Geometric Properties of Torsion Points -- Reduction mod p and Torsion Points -- Proof of Mordell's Finite Generation Theorem -- Galois Cohomology and Isomorphism Classification of Elliptic Curves over Arbitrary Fields -- Descent and Galois Cohomology -- Elliptic and Hypergeometric Functions -- Theta Functions -- Modular Functions -- Endomorphisms of Elliptic Curves -- Elliptic Curves over Finite Fields -- Elliptic Curves over Local Fields -- Elliptic Curves over Global Fields and l-adic Representations -- L-Functions of an Elliptic Curve and Its Analytic Continuation -- Remarks on the Birch and Swinnerton-Dyer Conjecture -- Remarks on the Modular Curves Conjecture and Fermat's Last Theorem -- Higher Dimensional Analogs of Elliptic Curves: Calabi-Yau Varieties -- Families of Elliptic Curves -- Appendix I: Calabi-Yau Manifolds and String Theory -- Appendix II: Elliptic Curves in Algorithmic Number Theory -- Appendix III: Guide to the Exercises.
  note: Dale Husemöller ; with appendices by Stefan Theisen, Otto Forster, and Ruth Lawrence.
  note: Electronic resource.
  note: Includes bibliographical references (pages 465-478) and index.
  subject:
    topic: Curves, Elliptic
  subject:
    topic: Curves, Algebraic
  subject:
    topic: Group schemes (Mathematics)
  subject:
    topic: Mathematics
  subject:
    topic: Algebraic Geometry
  subject:
    topic: MATHEMATICS
    topic: Geometry
    topic: Algebraic
  subject:
    topic: Curves, Algebraic
  subject:
    topic: Curves, Elliptic
  subject:
    topic: Group schemes (Mathematics)
  classification: QA567 .H897 2004eb
  classification: 516.3/52
  related item:
    title info:
      title: Elliptic curves
    name:
      name part: Husemöller, Dale.
    origin info:
      publisher: New York : Springer, ©2004
      edition: 2nd ed.
    identifier: (DLC) 2002067016
    identifier: (OCoLC)49672279
  related item:
    title info:
      title: Graduate texts in mathematics ; 111
  identifier: 0387215778
  identifier: 9780387215778
  identifier: 0387954902
  identifier: 9780387954905
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: N$T
    record creation date: 040731
    record change date: 20260420204352.7
    record identifier: in00003718438
    language of cataloging:
      language term: eng