03285cam a2200385 a 4500 16079467 OSt 20150408114015.0 100201s2010 enka b 001 0 eng 2010004489 GBB039433 bnb 015510910 Uk 9780521768795 (hardback) (OCoLC)ocn503072990 DLC DLC YDX BTCTA UKM YDXCP BWK CDX BWX IXA IUL DLC QA241 .K43 2010 512.74 22 Kedlaya, Kiran Sridhara, 1974- 14469 p-adic differential equations / Kiran S. Kedlaya. Cambridge ; New York : Cambridge University Press, 2010. xvii, 380 p. : ill. ; 24 cm. Cambridge studies in advanced mathematics ; 125 Includes bibliographical references and index. Norms on algebraic structures -- Newton polygons -- Ramification theory -- Matrix analysis -- Formalism of differential algebra -- Metric properties of differential modules -- Regular singularities -- Rings of functions on discs and annuli -- Radius and generic radius of convergence -- Frobenius pullback and pushforward -- Variation of generic and subsidiary radii -- Decomposition by subsidiary radii -- p-adic exponents -- Formalism of difference algebra -- Frobenius modules -- Frobenius modules over the Robba ring -- Frobenius structures on differential modules -- Effective convergence bounds -- Galois representations and differential modules -- The p-adic local monodromy theorem -- The p-adic local monodromy theorem: proof -- Picard-Fuchs modules -- Rigid cohomology -- p-adic Hodge theory. "Over the last 50 years the theory of p-adic differential equations has grown into an active area of research in its own right, and has important applications to number theory and to computer science. This book, the first comprehensive and unified introduction to the subject, improves and simplifies existing results as well as including original material. Based on a course given by the author at MIT, this modern treatment is accessible to graduate students and researchers. Exercises are included at the end of each chapter to help the reader review the material, and the author also provides detailed references to the literature to aid further study"--Provided by publisher. "Although the very existence of a highly developed theory of p-adic ordinary differential equations is not entirely well known even within number theory, the subject is actually almost 50 years old. Here are circumstances, past and present, in which it arises"-- Provided by publisher. p-adic analysis. 10564 Differential equations. Cambridge studies in advanced mathematics ; 125. 14470 Table of contents only http://www.loc.gov/catdir/enhancements/fy1006/2010004489-t.html Publisher description http://www.loc.gov/catdir/enhancements/fy1006/2010004489-d.html Contributor biographical information http://www.loc.gov/catdir/enhancements/fy1006/2010004489-b.html ddc BOOK 21592 256092 0 2013-03-10 0 0 512.74 K K P 2012-05-20 EMF 00086561 EMF 2013-03-10 00:00:00 BOOK ddc 0 0 2013-03-10 0 0 512.74 K K P 2012-05-20 EMF 00086562 EMF 2013-03-10 00:00:00 BOOK ddc 0 0 2013-03-10 0 0 512.74 K K P 2012-06-01 SZM 00086324 SZM 2013-03-10 00:00:00 BOOK ddc 0 0 2013-03-10 0 0 512.74 K K P 2012-06-01 SZM 00086323 SZM 2013-03-10 00:00:00 BOOK ddc 0 0 2013-03-10 0 0 512.74 K K P 2012-06-02 EZF 00086694 EZF 2013-03-10 00:00:00 BOOK ddc 0 0 2013-03-10 0 0 512.74 K K P 2012-06-02 EZF 00086695 EZF 2013-03-10 00:00:00 BOOK ddc 0 0 2013-03-10 0 0 512.74 K K P 2012-06-04 SHF 00088053 SHF 2013-03-10 00:00:00 BOOK ddc 0 0 2013-03-10 0 0 512.74 K K P 2012-06-04 SHF 00088054 SHF 2013-03-10 00:00:00 BOOK ddc 0