Topics in the theory of algebraic function fields /
[Book]
Gabriel Daniel Villa Salvador
Berlin :
Birkhäuser,
2006
xvi, 652 pages :
illustrations ;
24 cm
Mathematics : theory & applications
Textbook for graduates
Includes bibliographical references (pages [639]-646) and index
Preface.- 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.- Introduction to Class Field Theory.- Cyclotomic Function Fields.- Drinfeld Modules.- Automorphisms and Galois Theory.- Appendix A: Cohomology of Groups.- Notations.- References.- Index
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Presents an examination that explains both the similarities and fundamental differences between function fields and number fields, including many exercises and examples. This book serves as a text for a graduate course in number theory or an advanced graduate topics course
Introducción a la teoría de las funciones algebraicas.