p-adic Differential Equations
<I>p</I>-adic Differential Equations
$90.99
USDOver the last 50 years the theory of p-adic differential equations has grown into an active area of research in its own right, and has important applications to number theory and to computer science. This book, the first comprehensive and unified introduction to the subject, improves and simplifies existing results as well as including original material. Based on a course given by the author at MIT, this modern treatment is accessible to graduate students and researchers. Exercises are included at the end of each chapter to help the reader review the material, and the author also provides detailed references to the literature to aid further study.
- Assumes only an undergraduate-level course in abstract algebra
- Up-to-date treatment including previously unpublished results
- Class-tested by the author
Reviews & endorsements
'Before this book appeared, it was not easy for graduate students and researchers to study p-adic differential equations and related topics because on needed to read a lot of original papers. Now one can easily access these areas via this book.' Mathematical Reviews
Product details
May 2010Adobe eBook Reader
9780511741104
0 pages
0kg
1 b/w illus. 135 exercises
This ISBN is for an eBook version which is distributed on our behalf by a third party.
Table of Contents
- Preface
- Introductory remarks
- Part I. Tools of p-adic Analysis:
- 1. Norms on algebraic structures
- 2. Newton polygons
- 3. Ramification theory
- 4. Matrix analysis
- Part II. Differential Algebra:
- 5. Formalism of differential algebra
- 6. Metric properties of differential modules
- 7. Regular singularities
- Part III. p-adic Differential Equations on Discs and Annuli:
- 8. Rings of functions on discs and annuli
- 9. Radius and generic radius of convergence
- 10. Frobenius pullback and pushforward
- 11. Variation of generic and subsidiary radii
- 12. Decomposition by subsidiary radii
- 13. p-adic exponents
- Part IV. Difference Algebra and Frobenius Modules:
- 14. Formalism of difference algebra
- 15. Frobenius modules
- 16. Frobenius modules over the Robba ring
- Part V. Frobenius Structures:
- 17. Frobenius structures on differential modules
- 18. Effective convergence bounds
- 19. Galois representations and differential modules
- 20. The p-adic local monodromy theorem: Statement
- 21. The p-adic local monodromy theorem: Proof
- Part VI. Areas of Application:
- 22. Picard-Fuchs modules
- 23. Rigid cohomology
- 24. p-adic Hodge theory
- References
- Index of notation
- Index.
