Titlebook: Algebraic Functions and Projective Curves; David M. Goldschmidt Textbook 2003 Springer Science+Business Media New York 2003 Grad.algebraic

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Odyssey

Projective Curves,er that the ground field . is algebraically closed. Since we do not have at our disposal the machinery of algebraic geometry, our treatment here is necessarily somewhat ad hoc. The preferred approach to this subject is via the theory of schemes and varieties.

LAITY

essential-fats

0072-5285 on 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 a

HEAVY

Textbook 2003ce 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.

Congestion

0072-5285 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.978-0-387-22445-9Series ISSN 0072-5285 Series E-ISSN 2197-5612

期滿

Sarra Samet,Ridda Mohamed LaouarThis chapter contains some preliminary definitions and results needed in the sequel. Many of these results are quite elementary and well known, but in the self-contained spirit of the book, we have provided proofs rather than references. In this book the word “ring” means “commutative ring with identity,” unless otherwise explicitly stated.

PIZZA

Clumsy

Function Fields,lement, then . will be a finitely generated algebraic extension, i.e., a finite extension. Furthermore, we assume that . is algebraically closed in ., that is, that every element of . algebraic over . already lies in . In this situation, we say that . is a . over ., or sometimes that . is a function field.

細(xì)節(jié)

Projective Curves,er that the ground field . is algebraically closed. Since we do not have at our disposal the machinery of algebraic geometry, our treatment here is necessarily somewhat ad hoc. The preferred approach to this subject is via the theory of schemes and varieties.