Algebraic Functions and Projective Curves

  • David M. Goldschmidt

Part of the Graduate Texts in Mathematics book series (GTM, volume 215)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. David M. Goldschmidt
    Pages 1-39
  3. David M. Goldschmidt
    Pages 40-67
  4. David M. Goldschmidt
    Pages 68-102
  5. David M. Goldschmidt
    Pages 103-149
  6. David M. Goldschmidt
    Pages 150-163
  7. Back Matter
    Pages 164-185

About this book

Introduction

This book provides a self-contained exposition of the theory of algebraic curves without requiring any of the prerequisites of modern algebraic geometry. The self-contained treatment makes this important and mathematically central subject accessible to non-specialists. At the same time, specialists in the field may be interested to discover several unusual topics. Among these are Tates theory of residues, higher derivatives and Weierstrass points in characteristic p, the Stöhr--Voloch proof of the Riemann hypothesis, and a treatment of inseparable residue field extensions. Although the exposition is based on the theory of function fields in one variable, the book is unusual in that it also covers projective curves, including singularities and a section on plane curves.
David Goldschmidt has served as the Director of the Center for Communications Research since 1991. Prior to that he was Professor of Mathematics at the University of California, Berkeley.

Keywords

Grad algebraic curve algebraic geometry zeta function

Authors and affiliations

  • David M. Goldschmidt
    • 1
  1. 1.IDA Center for Communications Research—PrincetonPrincetionUSA

Bibliographic information

  • DOI https://doi.org/10.1007/b97844
  • Copyright Information Springer Science+Business Media New York 2003
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-2995-2
  • Online ISBN 978-0-387-22445-9
  • Series Print ISSN 0072-5285
  • Series Online ISSN 2197-5612
  • Buy this book on publisher's site