p-adic differential equations
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Main Author : | |
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Format : | Book |
Language : | anglais |
Title statement : | p-adic differential equations / Kiran S. Kedlaya,... |
Published : |
Cambridge, New York, Melbourne [etc.] :
Cambridge University Press
, cop. 2010 |
Physical Description : | 1 vol. (XVII-380 p.) |
Series : | Cambridge studies in advanced mathematics ; 125 |
Online Access : |
Lien vers la préface et la table des matières
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Subjects : |
- 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