p-adic Differential Equations
Published on 10. June 2010
Book
Hardback
398 pages
978-0-521-76879-5 (ISBN)
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.
Reviews / Votes
'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 ReviewsMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Illustrations
Worked examples or Exercises; 1 Line drawings, black and white
Dimensions
Height: 235 mm
Width: 158 mm
Thickness: 24 mm
Weight
680 gr
ISBN-13
978-0-521-76879-5 (9780521768795)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
New editions
Kiran S. Kedlaya
p-adic Differential Equations
Book
06/2022
2nd Edition
Cambridge University Press
€95.00
Shipment within 15-20 days
Additional editions
Kiran S. Kedlaya
p-adic Differential Equations
E-Book
05/2010
1st Edition
Cambridge University Press
€67.99
Available for download
Person
Kiran S. Kedlaya is Associate Professor of Mathematics at Massachusetts Institute of Technology, Cambridge, USA.
Content
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.