Abhyankar Ramification Theoretic Methods in Algebraic Geometry

1. Auflage 2016
ISBN: 978-1-4008-8139-0
Verlag: De Gruyter
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 43, 112 Seiten

Reihe: Annals of Mathematics Studies

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.

Autoren/Hrsg.

Abhyankar, Shreeram Shankar

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie

Inhaltsverzeichnis

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