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p-adic Differential Equations

£51.00

Part of Cambridge Studies in Advanced Mathematics

  • Date Published: June 2010
  • availability: Available
  • format: Hardback
  • isbn: 9780521768795

£ 51.00
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  • 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.

    • Assumes only an undergraduate-level course in abstract algebra
    • Up-to-date treatment including previously unpublished results
    • Class-tested by the author
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    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

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    Product details

    • Date Published: June 2010
    • format: Hardback
    • isbn: 9780521768795
    • length: 398 pages
    • dimensions: 235 x 158 x 24 mm
    • weight: 0.68kg
    • contains: 1 b/w illus. 135 exercises
    • availability: Available
  • 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.

  • Resources for

    p-adic Differential Equations

    Kiran S. Kedlaya

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  • Author

    Kiran S. Kedlaya, Massachusetts Institute of Technology
    Kiran S. Kedlaya is Associate Professor of Mathematics at Massachusetts Institute of Technology, Cambridge, USA.

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