Introductory Notes on Valuation Rings and Function Fields in One Variable
Authors: Scognamillo, Renata, Zannier, Umberto
- Provides the basic theory of valuation rings and shows applications to many issues treated only individually in other books
- Presents the theory of valuation rings in an elementary and general way and results that which are difficult to locate in the literature
- Gives several arithmetical applications of the main theory and other important results from geometry and number theory
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- About this Textbook
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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.
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Introductory Notes on Valuation Rings and Function Fields in One Variable
- Authors
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- Renata Scognamillo
- Umberto Zannier
- Series Title
- Lecture Notes (Scuola Normale Superiore)
- Series Volume
- 14
- Copyright
- 2014
- Publisher
- Edizioni della Normale
- Copyright Holder
- Edizioni della Normale
- eBook ISBN
- 978-88-7642-501-1
- DOI
- 10.1007/978-88-7642-501-1
- Softcover ISBN
- 978-88-7642-500-4
- Edition Number
- 1
- Number of Pages
- VIII, 119
- Topics
