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
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: xxu
    date issued: 2004
    edition: Second Edition.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XXII, 490 p. online resource.
  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: to Rational Points on Plane Curves -- Elementary Properties of the Chord-Tangent Group Law on a Cubic Curve -- Plane Algebraic Curves -- Elliptic Curves and Their Isomorphisms -- 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 ?-Adic Representations -- L-Function of an Elliptic Curve and Its Analytic Continuation -- Remarks on the Birch and Swinnerton-Dyer Conjecture -- Remarks on the Modular Elliptic Curves Conjecture and Fermat’s Last Theorem -- Higher Dimensional Analogs of Elliptic Curves: Calabi-Yau Varieties -- Families of Elliptic Curves.
  note: by Dale Husemöller.
  subject:
    topic: Mathematics
  subject:
    topic: Algebraic geometry
  subject:
    topic: Mathematics
  subject:
    topic: Algebraic Geometry
  classification: QA564-609
  classification: 516.35
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Graduate Texts in Mathematics, 111
  identifier: 9780387215778
  identifier: http://dx.doi.org/10.1007/b97292
  record info:
    record creation date: 100301
    record change date: 20151204160918.0
    record identifier: 978-0-387-21577-8