p-adic Differential Equations by Kiran S Kedlaya
Now in its second edition, this volume provides a uniquely detailed study of $P$-adic differential equations. Assuming only a graduate-level background in number theory, the text builds the theory from first principles all the way to the frontiers of current research, highlighting analogies and links with the classical theory of ordinary differential equations. The author includes many original results which play a key role in the study of $P$-adic geometry, crystalline cohomology, $P$-adic Hodge theory, perfectoid spaces, and algorithms for L-functions of arithmetic varieties. This updated edition contains five new chapters, which revisit the theory of convergence of solutions of $P$-adic differential equations from a more global viewpoint, introducing the Berkovich analytification of the projective line, defining convergence polygons as functions on the projective line, and deriving a global index theorem in terms of the Laplacian of the convergence polygon.
'… the book under review is unique in the sense that it can serve as a comprehensive introduction to the subject (the monograph assumes just a graduate-level background in algebraic number theory) and as a roadmap for researchers in the area' Alexander B. Levin, MathSciNet
Kiran S. Kedlaya is the Stefan E. Warschawski Professor of Mathematics at University of California, San Diego. He has published over 100 research articles in number theory, algebraic geometry, and theoretical computer science, as well as several books, including two on the Putnam competition. He has received a Presidential Early Career Award, a Sloan Fellowship, and a Guggenheim Fellowship, and been named an ICM invited speaker and a fellow of the American Mathematical Society.
| SKU | Unavailable |
| ISBN 13 | 9781009123341 |
| ISBN 10 | 1009123343 |
| Title | p-adic Differential Equations |
| Author | Kiran S Kedlaya |
| Series | Cambridge Studies In Advanced Mathematics |
| Condition | Unavailable |
| Publisher | Cambridge University Press |
| Year published | 2022-06-09 |
| Number of pages | 420 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |