Introductory Notes on Valuation Rings and Function Fields in One Variable (Paperback)

Introductory Notes on Valuation Rings and Function Fields in One Variable By Renata Scognamillo, Umberto Zannier Cover Image
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Description


The book deals with the (elementary and introductory) theory of valuation rings. As explained in the introduction, this represents a useful and important viewpoint in algebraic geometry, especially concerning the theory of algebraic curves and their function fields. The correspondences of this with other viewpoints (e.g. of geometrical or topological nature) are often indicated, also to provide motivations and intuition for many results. Links with arithmetic are also often indicated. There are three appendices, concerning Hilbert's Nullstellensatz (for which several proofs are provided), Puiseux series and Dedekind domains. There are also several exercises, often accompanied by hints, which sometimes develop further results not included in full for brevity reasons.


Product Details
ISBN: 9788876425004
ISBN-10: 8876425004
Publisher: Edizioni Della Normale
Publication Date: May 11th, 2015
Pages: 119
Language: English
Series: Publications of the Scuola Normale Superiore / Lecture Notes