Introduction to the theory of algebraic functions of one variable
Author(s)
Bibliographic Information
Introduction to the theory of algebraic functions of one variable
（Mathematical surveys, no. 6）
American Mathematical Society, 1951
Available at / 88 libraries
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science研究室
DC16:512.8/C4270025382575
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Note
Includes index
Description and Table of Contents
Description
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.
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