Algebraic Functions and Projective Curves

2003
ISBN: 978-0-387-95432-5
Verlag: Springer

Buch, Englisch, 185 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 1030 g

Reihe: Graduate Texts in Mathematics

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.

Zielgruppe

Graduate

Autoren/Hrsg.

Goldschmidt, David

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Zahlentheorie
• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie

Inhaltsverzeichnis

Background.- Function Fields.- Finite Extensions.- Projective Curves.- Zeta Functions.