Algebraic Functions and Projective Curves
(Sprache: Englisch)
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...
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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. 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.
Inhaltsverzeichnis zu „Algebraic Functions and Projective Curves “
Preface Introduction Background Function Fields Finite Extensions Projective Curves Zeta Functions Appendix: Elementary Field Theory References Index
Bibliographische Angaben
- Autor: David Goldschmidt
- 2010, 185 Seiten, Maße: 22,9 cm, Kartoniert (TB), Englisch
- Verlag: Springer, New York
- ISBN-10: 1441929959
- ISBN-13: 9781441929952
Sprache:
Englisch
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