(Ebook) p-adic Differential Equations by Kiran S. Kedlaya ISBN 9780521768795, 0521768799, B01DM25HJQ

(Ebook) p-adic Differential Equations by Kiran S. Kedlaya ISBN 9780521768795, 0521768799, B01DM25HJQ

Main subject categories: • Number theory • Differential equations • p-adic differential equations • Tools of p-adic analysis • Norms on algebraic structures • Newton polygons • Ramification theory • Matrix analysis • Differential algebra • p-adic differential equations on discs and annuli • Difference algebra and Frobenius modules • Frobenius structures • The p-adic local monodromy theorem • Global theoryOver 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.