UID:
almahu_9949366512502882
Format:
1 online resource (xx, 496 pages) :
,
digital, PDF file(s).
Edition:
Second edition.
ISBN:
9781009127684 (ebook)
Series Statement:
Cambridge studies in advanced mathematics ; 198
Content:
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.
Note:
Title from publisher's bibliographic system (viewed on 08 Aug 2022).
Additional Edition:
Print version: ISBN 9781009123341
Language:
English
URL:
https://doi.org/10.1017/9781009127684
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