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p-adic Differential Equations
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p-adic Differential Equations

2 Revised edition

by Kiran S. Kedlaya

Book Details

Format Hardback or Cased Book
Book Series Cambridge Studies in Advanced Mathematics
ISBN-10 1009123343
ISBN-13 9781009123341
Edition 2 Revised edition
Publisher Cambridge University Press
Imprint Cambridge University Press
Country of Manufacture GB
Country of Publication GB
Publication Date Jun 9th, 2022
Print length 420 Pages
Weight 856 grams
Dimensions 15.90 x 23.60 x 4.30 cms
Product Classification: Number theory Differential calculus & equations
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This book surveys the theory of $P$-adic differential equations, from the foundations of $P$-adic numbers to the current frontiers of research. It assumes only a graduate-level background in number theory, and includes detailed chapter notes as well as numerous exercises. This second edition features new material on global theory.
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.

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