| Description |
1 online resource (xvii, 380 pages) : illustrations |
| Series |
Cambridge studies in advanced mathematics ; 125 |
|
Cambridge studies in advanced mathematics ; 125.
|
| Contents |
Norms on algebraic structures -- Newton polygons -- Ramification theory -- Matrix analysis -- Formalism of differential algebra -- Metric properties of differential modules -- Regular singularities -- Rings of functions on discs and annuli -- Radius and generic radius of convergence -- Frobenius pullback and pushforward -- Variation of generic and subsidiary radii -- Decomposition by subsidiary radii -- p-adic exponents -- Formalism of difference algebra -- Frobenius modules -- Frobenius modules over the Robba ring -- Frobenius structures on differential modules -- Effective convergence bounds -- Galois representations and differential modules -- The p-adic local monodromy theorem -- The p-adic local monodromy theorem: proof -- Picard-Fuchs modules -- Rigid cohomology -- p-adic Hodge theory |
| Summary |
"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"-- Provided by publisher |
|
"Although the very existence of a highly developed theory of p-adic ordinary differential equations is not entirely well known even within number theory, the subject is actually almost 50 years old. Here are circumstances, past and present, in which it arises"-- Provided by publisher |
| Bibliography |
Includes bibliographical references and index |
| Notes |
English |
|
Print version record |
| Subject |
p-adic analysis.
|
|
Differential equations.
|
|
MATHEMATICS -- Number Theory.
|
|
Differential equations
|
|
p-adic analysis
|
| Form |
Electronic book
|
| LC no. |
2010004489 |
| ISBN |
9780511750182 |
|
0511750188 |
|
9780511744723 |
|
0511744722 |
|
9780511743634 |
|
0511743637 |
|
9780511750922 |
|
0511750927 |
|
1107209293 |
|
9781107209299 |
|
1282631683 |
|
9781282631687 |
|
9786612631689 |
|
6612631686 |
|
0511749449 |
|
9780511749445 |
|
0511742568 |
|
9780511742569 |
|
