Ramification Theoretic Methods in Algebraic Geometry
1st Edition
Published on 20. June 2016
112 pages
978-1-4008-8139-0 (ISBN)
Description
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.
To mark the continued success of the series, all books are available in paperback and as ebooks.
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.
To mark the continued success of the series, all books are available in paperback and as ebooks.
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Shreeram Shankar Abhyankar
Ramification Theoretic Methods in Algebraic Geometry
Book
07/1959
Princeton University Press
€50.90
Available immediately
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Shreeram Shankar Abhyankar
Content
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
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
