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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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p-Adic Automorphic Forms on Shimura Varieties (Springer Monographs in Mathematics), Elliptic Curves and Arithmetic Invariants, Geometric Modular Forms and Elliptic Curves, Modular Forms and Galois Cohomology, Geometric Modular Forms and Elliptic Cur, P-Adic Automorphic Forms on Shimura Varieties, Contributions to Automorphic Forms, Geometry, and Number Theory: A Volume in Honor of Joseph Shalika, Elementary Theory of L-Functions and Eisenstein Series, Modular Forms and Galois Cohomology, Hilbert Modular Forms and Iwasawa Theory
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, The approach is basically algebraic and the treatment elementary in this comprehensive and systematic account of the theory of p adic and classical modular forms and the theory of the special values of arithmetic L functions and p adic, In i Contributions to Automorphic Forms Geometry and Number Theory i Haruzo Hida Dinakar Ramakrishnan and Freydoon Shahidi bring together a distinguished group of experts to explore automorphic forms principally via the associated L functions representation theory and geometry Because these themes are at the cutting edge of a central area of modern mathematics and are related to the philosophical base of Wiles proof of Fermat s last theorem this book will be of interest to working mathematicians and students alike Never previously published the contributions to this volume expose the reader to a host of difficult and thought provoking problems br br Each of the extraordinary and noteworthy mathematicians in this volume makes a unique contribution to a field that is currently seeing explosive growth New and powerful results are being proved radically and continually changing the field s make up i Contributions to Automorphic Forms Geometry and Number Theory i will likely lead to vital interaction among researchers and also help prepare students and other young mathematicians to enter this exciting area of pure mathematics br br Contributors Jeffrey Adams Jeffrey D Adler James Arthur Don Blasius Siegfried Boecherer Daniel Bump William Casselmann Laurent Clozel James Cogdell Laurence Corwin Solomon Friedberg Masaaki Furusawa Benedict Gross Thomas Hales Joseph Harris Michael Harris Jeffrey Hoffstein Herv Jacquet Dihua Jiang Nicholas Katz Henry Kim Victor Kreiman Stephen Kudla Philip Kutzko V Lakshmibai Robert Langlands Erez Lapid Ilya Piatetski Shapiro Dipendra Prasad Stephen Rallis Dinakar Ramakrishnan Paul Sally Freydoon Shahidi Peter Sarnak Rainer Schulze Pillot Joseph Shalika David Soudry Ramin Takloo Bigash Yuri Tschinkel Emmanuel Ullmo Marie France Vign ras Jean Loup Waldspurger, 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