Format:
1 Online-Ressource (xx, 496 Seiten)
Edition:
Second edition
ISBN:
9781009127684
Series Statement:
Cambridge studies in advanced mathematics 199
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:
Erscheint auch als Druck-Ausgabe ISBN 978-1-00-912334-1
Language:
English
Subjects:
Mathematics
Keywords:
p-adische Differentialgleichung
;
p-adische Analysis
DOI:
10.1017/9781009127684
URL:
Volltext
(URL des Erstveröffentlichers)
