Algebraic Functions and Projective Curves (Graduate Texts in Mathematics, 215) - Hardcover

Goldschmidt, David

Hardcover

ISBN 10: 0387954325 ISBN 13: 9780387954325

Publisher: Springer, 2002

Synopsis

This book gives an introduction to algebraic functions and projective curves. It covers a wide range of material by dispensing with the machinery of algebraic geometry and proceeding directly via valuation theory to the main results on function fields. It also develops the theory of singular curves by studying maps to projective space, including topics such as Weierstrass points in characteristic p, and the Gorenstein relations for singularities of plane curves.

About this title

From the Back Cover

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.

Edition details

• Publisher: Springer
• Publication date: 2002
• Language: English
• ISBN 10: 0387954325
• ISBN 13: 9780387954325
• Binding: Hardcover
• Number of pages: 201