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A classic treatment of ramification theoretic methods in algebraic geometry from the acclaimed Annals of Mathematics Studies series
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List of contents
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
About the author
Shreeram Shankar Abhyankar
Summary
The description for this book, Ramification Theoretic Methods in Algebraic Geometry (AM-43), will be forthcoming.
