(Ebook) p-adic Differential Equations: Second Edition by Kiran S. Kedlaya ISBN 9781009123341, 1009123343, B0B1V3FGMZ

(Ebook) p-adic Differential Equations: Second Edition by Kiran S. Kedlaya ISBN 9781009123341, 1009123343, B0B1V3FGMZ

Main subject categories: • Number theory • Differential equations • p-adic differential equations • Tools of p-adic analysis • Norms on algebraic structures • Newton polygons • Ramification theory • Matrix analysis • Differential algebra • p-adic differential equations on discs and annuli • Difference algebra and Frobenius modules • Frobenius structures • The p-adic local monodromy theorem • Global theoryNow 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.