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SUMMARY:P-adic families of automorphic forms - David Loeffler (Imperial)
DTSTART:20080219T143000Z
DTEND:20080219T153000Z
UID:TALK10792@talks.cam.ac.uk
CONTACT:Tim Dokchitser
DESCRIPTION:In this talk\, I will discuss some of the remarkable p-adic co
 ntinuity\nproperties of automorphic forms. For classical modular forms\, i
 t was\nnoted early on that there appear to exist p-adic families of Hecke\
 neigenforms -- q-expansions with coefficients that are formal power\nserie
 s in a variable k\, which if evaluated at (some) positive integers k\nconv
 erge p-adically to the q-expansion of a Hecke eigenform.\n\nIn the 1990s C
 oleman and Mazur showed that all modular forms of finite\nslope may be int
 erpolated in this way\, and constructed a p-adic rigid\nspace\, the eigenc
 urve\, which can be regarded as a parameter space for\nsuch families. I sh
 all give an introduction to the Coleman-Mazur theory\,\nand describe some 
 current research on analogous results for automorphic\nforms on higher-ran
 k groups.\n
LOCATION:MR13
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