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Introductory Notes on Valuation Rings and Function Fields in One Variable

Introductory Notes on Valuation Rings and Function Fields in One Variable by Renata Scognamillo
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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.
Scuola Normale Superiore; July 2014
125 pages; ISBN 9788876425011
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Title: Introductory Notes on Valuation Rings and Function Fields in One Variable
Author: Renata Scognamillo; Umberto Zannier
 
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