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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations
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p-adic Differential Equations (Hardcover, 2nd Revised edition)
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p-adic Differential Equations (Hardcover, 2nd Revised edition)
Series: Cambridge Studies in Advanced Mathematics
Expected to ship within 12 - 17 working days
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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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