Description

Book Synopsis
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.

Table of Contents
Generalities on function fields of one variable.- Valuation rings.- Completions.- Appendices on Hilbert's Nullstellensatz, Puiseux series, Dedekind domains.

Introductory Notes on Valuation Rings and Function Fields in One Variable

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    A Paperback by Renata Scognamillo, Umberto Zannier

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      View other formats and editions of Introductory Notes on Valuation Rings and Function Fields in One Variable by Renata Scognamillo

      Publisher: Birkhauser Verlag AG
      Publication Date: 11/05/2015
      ISBN13: 9788876425004, 978-8876425004
      ISBN10: 8876425004

      Description

      Book Synopsis
      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.

      Table of Contents
      Generalities on function fields of one variable.- Valuation rings.- Completions.- Appendices on Hilbert's Nullstellensatz, Puiseux series, Dedekind domains.

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