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SUMMARY:On the local mod p representation attached to a modular form - Kev
 in Buzzard (Imperial)
DTSTART:20130122T161500Z
DTEND:20130122T171500Z
UID:TALK42675@talks.cam.ac.uk
CONTACT:Teruyoshi Yoshida
DESCRIPTION:There is a 2-dimensional p-adic Galois representation attached
  to any modular form which is an eigenform for the Hecke operators. One ca
 n reduce it mod p and get an even simpler object - a mod p Galois represen
 tation\, which will have finite image. One would have thought that nowaday
 s essentially everything was known about this representation\, but actuall
 y there are still some dangling issues at p. For example - if I give you a
 n explicit modular form (e.g. via its q-expansion)\, is the associated loc
 al mod p representation reducible or irreducible? This question is local\,
  but still poorly understood. I will explain what little I know\, most of 
 which is joint work with Toby Gee. In what looks like a sledgehammer-crack
 ing-a-nut approach\, we invoke recent deep work of Breuil-Berger and other
 s on the p-adic and mod p Langlands philosophy for GL(2) to get some concr
 ete down-to-earth results.
LOCATION:MR14
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