p-adic Differential Equations

Kiran S. Kedlaya (University of California, San Diego)

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English

Cambridge University Press
09 June 2022

Number theory; Differential calculus & equations

Series: Cambridge Studies in Advanced Mathematics

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.

By: Kiran S. Kedlaya (University of California San Diego)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Edition: 2nd Revised edition
Dimensions: Height: 235mm, Width: 157mm, Spine: 33mm
Weight: 910g
ISBN: 9781009123341
ISBN 10: 1009123343
Series: Cambridge Studies in Advanced Mathematics
Pages: 420
Publication Date: 09 June 2022
Audience: General/trade , ELT Advanced
Format: Hardback
Publisher's Status: Active

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.

Reviews for p-adic Differential Equations

'… 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