p-adic differential equations

Author(s)

• Kedlaya, Kiran Sridhara

Bibliographic Information

p-adic differential equations

Kiran S. Kedlaya

（Cambridge studies in advanced mathematics, 125）

Cambridge University Press, 2010

• : hardback

Note

Includes bibliographical references (p. 365-373) and index

Description and Table of Contents

Description

Over 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.

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.

by "Nielsen BookData"

Details

• NCID: BB02372062
• ISBN:
  • 9780521768795
• LCCN: 2010004489
• Country Code: uk
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Cambridge
• Pages/Volumes: xvii, 380 p.
• Size: 24 cm
• Classification:
  • LCC : QA241
  • DC22 : 512.7/4
• Subject Headings:
  • LCSH : p-adic analysis
  • LCSH : Differential equations
• Parent Bibliography ID:
  • BA00109761