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: Diophantine geometry
    sub title: an introduction
  name:
    name part: Hindry, Marc.
    role:
      role term: creator
  name:
    name part: Silverman, Joseph H.
    name part: 1955-
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  genre: bibliography
  genre: Electronic books.
  origin info:
    place:
      place term: nyu
    date issued: 2000
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: remote
    extent: 1 online resource (xiii, 558 pages) : illustrations.
  abstract: "Diophantine geometry is the study of integral and rational solutions to systems of polynomial equations using ideas and techniques from algebraic number theory and algebraic geometry. The ultimate goal is to describe the solutions in terms of geometric invariants of the underlying algebraic variety. This book contains complete proofs of four of the fundamental finiteness theorems in Diophantine geometry."--BOOK JACKET.
  table of contents: Part A Geometry of Curves and Abelian Varieties 6 -- A.1 Algebraic Varieties 8 -- A.2 Divisors 34 -- A.3 Linear Systems 49 -- A.4 Algebraic Curves 67 -- A.5 Abelian Varieties over C 91 -- A.6 Jacobians over C 110 -- A.7 Abelian Varieties over Arbitrary Fields 119 -- A.8 Jacobians over Arbitrary Fields 134 -- A.9 Schemes 151 -- Part B Height Functions 168 -- B.1 Absolute Values 170 -- B.2 Heights on Projective Space 174 -- B.3 Heights on Varieties 183 -- B.4 Canonical Height Functions 195 -- B.5 Canonical Heights on Abelian Varieties 199 -- B.6 Counting Rational Points on Varieties 210 -- B.7 Heights and Polynomials 224 -- B.8 Local Height Functions 237 -- B.9 Canonical Local Heights on Abelian Varieties 241 -- B.10 Introduction to Arakelov Theory 243 -- Part C Rational Points on Abelian Varieties 257 -- C.1 Weak Mordell-Weil Theorem 260 -- C.2 Kernel of Reduction Modulo p 267 -- C.3 Appendix Finiteness Theorems in Algebraic Number Theory 273 -- C.4 Appendix Selmer and Tate-Shafarevich Groups 279 -- C.5 Appendix Galois Cohomology and Homogeneous Spaces 283 -- Part D Diophantine Approximation and Integral Points on Curves 299 -- D.1 Two Elementary Results on Diophantine Approximation 300 -- D.2 Roth's Theorem 304 -- D.3 Preliminary Results 307 -- D.4 Construction of the Auxiliary Polynomial 316 -- D.5 Index Is Large 323 -- D.6 Index Is Small (Roth's Lemma) 329 -- D.7 Completion of the Proof of Roth's Theorem 341 -- D.8 Application: The Unit Equation U + V = 1 345 -- D.9 Application: Integer Points on Curves 353 -- Part E Rational Points on Curves of Genus at Least 2 367 -- E.1 Vojta's Geometric Inequality and Faltings' Theorem 369 -- E.2 Pinning Down Some Height Functions 373 -- E.3 An Outline of the Proof of Vojta's Inequality 379 -- E.4 An Upper Bound for h[subscript Omega](z, w) 381 -- E.5 A Lower Bound for h[subscript Omega](z, w) for Nonvanishing Sections 385 -- E.6 Constructing Sections of Small Height I: Applying Riemann-Roch 389 -- E.7 Constructing Sections of…
  note: Marc Hindry, Joseph H. Silverman.
  note: Includes bibliographical references (pages [504]-519) and index.
  subject:
    topic: Arithmetical algebraic geometry
  subject:
    topic: point rationnel
  subject:
    topic: courbe géométrique
  subject:
    topic: variété abélienne
  subject:
    topic: géométrie diophantienne
  subject:
    topic: Géométrie algébrique arithmétique
  subject:
    topic: Diofantische analyse
  subject:
    topic: Géométrie algébrique arithmétique
  subject:
    topic: Arithmetical algebraic geometry
  classification: QA242.5 .H56 2000eb
  classification: 512/.7
  classification: 31.51
  related item:
    title info:
      title: Diophantine geometry
    name:
      name part: Hindry, Marc.
    identifier: (DLC) 99057467
    identifier: (OCoLC)42810847
  related item:
    title info:
      title: Graduate texts in mathematics ; 201
  identifier: 9781461212102 (electronic bk.)
  identifier: 1461212103 (electronic bk.)
  identifier: 0387989757
  identifier: 9780387989754
  identifier: 0387989811
  identifier: 9780387989815
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: GW5XE
    record creation date: 140711
    record change date: 20260422210549.0
    record identifier: in00003554230
    language of cataloging:
      language term: eng