✦ LIBER ✦

Introduction to the theory of algebraic functions of one variable

✍ Scribed by Claude Chevalley

Book ID: 127454313
Publisher: American Mathematical Society
Year: 1951
Tongue: English
Weight: 10 MB
Series: Mathematical Surveys and Monographs
Edition: 1st
Category: Library
ISBN: 0821815067
ASIN: B000UG78JA

No coin nor oath required. For personal study only.

✦ Synopsis

This classical book, written by a famous French mathematician in the early 1950s, presents an approach to algebraic geometry of curves treated as the theory of algebraic functions on the curve. Among other advantages of such an approach, it allowed the author to consider curves over an arbitrary ground field. Among topics discussed in the book are the theory of divisors on a curve, the Riemann-Roch theorem, $p$-adic completion, extensions of the fields of functions (covering theory) and of the fields of constants, and the theory of differentials on a curve. The last chapter, which is more analytic in flavor, treats the theory of Riemann surfaces. Prerequisites for reading are minimal and include only an advanced undergraduate algebra course.