Description

Book Synopsis

The description for this book, Ramification Theoretic Methods in Algebraic Geometry (AM-43), will be forthcoming.



Table 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

Ramification Theoretic Methods in Algebraic

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    A Paperback by Shreeram Shanka Abhyankar

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      Publisher: Princeton University Press
      Publication Date: Publication Date: 8/5/1994 12:00:00 AM
      ISBN13: 9780691080239, 978-0691080239
      ISBN10: 0691080232
      Also in:
      Mathematics Algebra

      Description

      Book Synopsis

      The description for this book, Ramification Theoretic Methods in Algebraic Geometry (AM-43), will be forthcoming.



      Table 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

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