Topics in the Theory of Algebraic Function Fields

• Main Author: Villa Salvador, Gabriel Daniel (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Boston, MA : Birkhäuser Boston, 2006.
• Series: Mathematics: Theory & Applications
• Subjects: Mathematics.; Algebraic geometry.; Commutative algebra.; Commutative rings.; Algebra.; Field theory (Physics).; Mathematical analysis.; Analysis (Mathematics).; Functions of complex variables.; Number theory.; Number Theory.; Functions of a Complex Variable.; Algebraic Geometry.; Field Theory and Polynomials.; Analysis.; Commutative Rings and Algebras.

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...

Table of Contents:

• 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.