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

Buch 63 von 180: Graduate Texts in Mathematics

Goldschmidt, David

 
9780387954325: Algebraic Functions and Projective Curves (Graduate Texts in Mathematics, 215, Band 215)
Hardcover
ISBN 10: 0387954325 ISBN 13: 9780387954325
Verlag: Springer, 2002

Inhaltsangabe

This book grew out of a set of notes for a series of lectures I orginally gave at the Center for Communications Research and then at Princeton University. The motivation was to try to understand the basic facts about algebraic curves without the modern prerequisite machinery of algebraic geometry. Of course, one might well ask if this is a good thing to do. There is no clear answer to this question. In short, we are trading off easier access to the facts against a loss of generality and an impaired understanding of some fundamental ideas. Whether or not this is a useful tradeoff is something you will have to decide for yourself. One of my objectives was to make the exposition as self-contained as possible. Given the choice between a reference and a proof, I usually chose the latter. - though I worked out many of these arguments myself, I think I can con?dently predict that few, if any, of them are novel. I also made an effort to cover some topics that seem to have been somewhat neglected in the expository literature.

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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.

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Verlag
Springer
Erscheinungsdatum
2002
Sprache
Englisch
ISBN 10 
0387954325
ISBN 13 
9780387954325
Einband
Gebundene Ausgabe
Anzahl der Seiten
201
Kontakt zum Hersteller
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Hamburg
22391
Deutschland

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Softcover