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p-adic Differential Equations

Kiran S. Kedlaya
Publisher: 
Cambridge University Press
Publication Date: 
2010
Number of Pages: 
380
Format: 
Hardcover
Series: 
Cambridge Studies in Advanced Mathematics 125
Price: 
75.00
ISBN: 
9780521768795
Category: 
Monograph
We do not plan to review this book.

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.

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