Topics in the Theory of Algebraic Function Fields

The fields of algebraic functions of one variable appear in several areas of mathematics: complex analysis, algebraic geometry, and number theory. This text adopts the latter perspective by applying an arithmetic-algebraic viewpoint to the study of function fields as part of the algebraic theory of...

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Détails bibliographiques
Cote:Libro Electrónico
Auteur principal: Villa Salvador, Gabriel Daniel (Auteur)
Collectivité auteur: SpringerLink (Online service)
Format: Électronique eBook
Langue:Inglés
Publié: Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, 2006.
Édition:1st ed. 2006.
Collection:Mathematics: Theory & Applications
Sujets:
Number theory.
Functions of complex variables.
Algebraic geometry.
Algebraic fields.
Polynomials.
Mathematical analysis.
Commutative algebra.
Commutative rings.
Number Theory.
Functions of a Complex Variable.
Algebraic Geometry.
Field Theory and Polynomials.
Analysis.
Commutative Rings and Algebras.
Accès en ligne:Texto Completo
Table des matières:
  • Algebraic and Numerical Antecedents
  • Algebraic Function Fields of One Variable
  • The Riemann-Roch Theorem
  • Examples
  • Extensions and Galois Theory
  • Congruence Function Fields
  • The Riemann Hypothesis
  • Constant and Separable Extensions
  • The Riemann-Hurwitz Formula
  • Cryptography and Function Fields
  • to Class Field Theory
  • Cyclotomic Function Fields
  • Drinfeld Modules
  • Automorphisms and Galois Theory.

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