Lecture Notes (Scuola Normale Superiore)

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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eBook 20,22 €
price for Spain (gross)
  • ISBN 978-88-7642-501-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 24,96 €
price for Spain (gross)
  • ISBN 978-88-7642-500-4
  • Free shipping for individuals worldwide
  • Online orders shipping within 2-3 days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this Textbook

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 (3 chapters)

  • Introduction Generalities on algebraic functions of one variabile

    Scognamillo, Renata (et al.)

    Pages 1-6

    Preview Buy Chapter 30,19 €
  • Basic notions on function fields of one variable

    Scognamillo, Renata (et al.)

    Pages 7-29

    Preview Buy Chapter 30,19 €
  • Valuation rings

    Scognamillo, Renata (et al.)

    Pages 31-84

    Preview Buy Chapter 30,19 €

Buy this book

eBook 20,22 €
price for Spain (gross)
  • ISBN 978-88-7642-501-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 24,96 €
price for Spain (gross)
  • ISBN 978-88-7642-500-4
  • Free shipping for individuals worldwide
  • Online orders shipping within 2-3 days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Introductory Notes on Valuation Rings and Function Fields in One Variable
Authors
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