p-Adic Automorphic Forms on Shimura Varieties

di Haruzo Hida (Autore)

Springer-Verlag New York Inc., 2004

In the early years of the 1980s, 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 10 to 15 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 15 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 2000 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.

• Autore: Haruzo Hida
• Editore: Springer-Verlag New York Inc.
• Collana: Springer Monographs in Mathematics
• Anno: 2004
• Rilegatura: Hardback
• Pagine: 390 p.
• Dimensioni: 235 x 155 mm
• EAN: 9780387207117

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