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Title:P-Adic Automorphic Forms on Shimura Varieties
Format Type:Ebook
Author:
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

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Elliptic Curves and Arithmetic Invariants, Geometric Modular Forms and Elliptic Cur, p-Adic Automorphic Forms on Shimura Varieties (Springer Monographs in Mathematics), Modular Forms and Galois Cohomology, Hilbert Modular Forms and Iwasawa Theory, Geometric Modular Forms and Elliptic Curves, Modular Forms and Galois Cohomology, Contributions to Automorphic Forms, Geometry, and Number Theory: A Volume in Honor of Joseph Shalika, Elementary Theory of L-Functions and Eisenstein Series, 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, This book contains a detailed account of the result of the author s recent Annals paper and JAMS paper on arithmetic invariant including u invariant L invariant and similar topics This book can be regarded as an introductory text to the author s previous book p Adic Automorphic Forms on Shimura Varieties Written as a down to earth introduction to Shimura varieties this text includes many examples and applications of the theory that provide motivation for the reader Since it is limited to modular curves and the corresponding Shimura varieties this book is not only a great resource for experts in the field but it is also accessible to advanced graduate students studying number theory Key topics include non triviality of arithmetic invariants and special values of L functions elliptic curves over complex and p adic fields Hecke algebras scheme theory elliptic and modular curves over rings and Shimura curves, The work of Wiles and Taylor Wiles opened up a whole new technique in algebraic number theory and a decade on the waves caused by this incredibly important work are still being felt This book authored by a leading researcher describes the striking applications that have been found for this technique In the book the deformation theoretic techniques of Wiles Taylor are first generalized to Hilbert modular forms following Fujiwara s treatment and some applications found by the author are then discussed With many exercises and open questions given this text is ideal for researchers and graduate students entering this research area br, No description available