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Title:P-Adic Automorphic Forms on Shimura Varieties
Format Type:Ebook
Author:Haruzo Hida
Publisher:Springer
ISBN:0387207112
ISBN 13:
Number of Pages:390
Category:Manga

P-Adic Automorphic Forms on Shimura Varieties by Haruzo Hida

PDF, EPUB, MOBI, TXT, DOC P-Adic Automorphic Forms on Shimura Varieties In the early years of the s while I was visiting the Institute for Ad vanced Study lAS at Princeton as a postdoctoral member I got a fascinating view studying congruence modulo a prime among elliptic modular forms that an automorphic L function of a given algebraic group G should have a canon ical p adic counterpart of several variables I immediately decided to find out the reason behind this phenomenon and to develop the theory of ordinary p adic automorphic forms allocating to years from that point putting off the intended arithmetic study of Shimura varieties via L functions and Eisenstein series for which I visited lAS Although it took more than years we now know at least conjecturally the exact number of variables for a given G and it has been shown that this is a universal phenomenon valid for holomorphic automorphic forms on Shimura varieties and also for more general nonholomorphic cohomological automorphic forms on automorphic manifolds in a markedly different way When I was asked to give a series of lectures in the Automorphic Semester in the year at the Emile Borel Center Centre Emile Borel at the Poincare Institute in Paris I chose to give an exposition of the theory of p adic ordinary families of such automorphic forms p adic analytically de pending on their weights and this book is the outgrowth of the lectures given there

Elementary Theory of L-Functions and Eisenstein Series, Geometric Modular Forms and Elliptic Curves, P-Adic Automorphic Forms on Shimura Varieties, Contributions to Automorphic Forms, Geometry, and Number Theory: A Volume in Honor of Joseph Shalika, Elliptic Curves and Arithmetic Invariants, Hilbert Modular Forms and Iwasawa Theory, Modular Forms and Galois Cohomology, p-Adic Automorphic Forms on Shimura Varieties (Springer Monographs in Mathematics), Geometric Modular Forms and Elliptic Cur, Modular Forms and Galois Cohomology