Książki

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 numbers. The examination explains both the similarities and fundamental differences between function fields and number fields, including many exercises and examples to enhance understanding and motivate further study. The only prerequisites are a basic knowledge of field theory, complex analysis, and some commutative algebra.

Topics in the Theory of Algebraic Function Fields

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.