Shreeram Shankar Abhyankar

Ramification Theoretic Methods in Algebraic Geometry (eBook, PDF)

• Format: PDF

Produktbeschreibung

A classic treatment of ramification theoretic methods in algebraic geometry from the acclaimed Annals of Mathematics Studies series

Princeton University Press is proud to have published the Annals of Mathematics Studies since 1940. One of the oldest and most respected series in science publishing, it has included many of the most important and influential mathematical works of the twentieth century. The series continues this tradition as Princeton University Press publishes the major works of the twenty-first century.

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Produktdetails

• Verlag: Princeton University Press
• Erscheinungstermin: 2. März 2016
• Englisch
• ISBN-13: 9781400881390
• Artikelnr.: 44908128

Autorenporträt

Shreeram Shankar Abhyankar

Inhaltsangabe

Preface
Introduction
I. General Ramification Theory
1. Elementary lemmas from ideal theory
2. Primary decomposition in non-noetherian rings
3. Integral dependence
4. Linear algebra
5. Discriminant of an algebra
6. The discriminant ideal
7. Galois theory of local rings
II. Valuation Theory
8. Ordered abelian groups
9. Valuations
10. Specialization and composition of valuations
11. Ramification theory of valuations
12. Valuations of algebraic function fields
III. Noetherian Local Rings
13. The dimension of a noetherian local ring
14. Quadratic transforms
IV. Two-Dimensional Local Domains
15. Limits of quadratic sequences
16. Uniformization in a two-dimensional regular local domain
17. Uniformization for a two-dimensional algebraic function field
V. Varieties and Transformations
18. Projective varieties
19. Resolution of singularities of algebraic surfaces
Bibliography