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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:p-adically completed cohomology and the p-adic Lan
glands program - Emerton\, M (Northwestern)
DTSTART;TZID=Europe/London:20090730T100000
DTEND;TZID=Europe/London:20090730T110000
UID:TALK19266AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/19266
DESCRIPTION:Speaking at a general level\, a major goal of the
p-adic Langlands program (from a global\, rather t
han local\, perspective) is to find a p-adic gener
alization of the notion of automorphic eigenform\,
the hope being that every p-adic global Galois re
presentation will correspond to such an object. (R
ecall that only those Galois representations that
are motivic\, i.e. that come from geometry\, are e
xpected to correspond to classical automorphic eig
enforms). \n\nIn certain contexts (namely\, when o
ne has Shimura varieties at hand)\, one can begin
with a geometric definition of automorphic forms\,
and generalize it to obtain a geometric definitio
n of p-adic automorphic forms. However\, in the no
n-Shimura variety context\, such an approach is no
t available. Furthermore\, this approach is somewh
at remote from the representation-theoretic point
of view on automorphic forms\, which plays such an
important role in the classical Langlands program
. \n\nIn this talk I will explain a different\, an
d very general\, approach to the problem of p-adic
interpolation\, via the theory of p-adically comp
leted cohomology. This approach has close ties to
the p-adic and mod p representation theory of p-ad
ic groups\, and to non-commutative= Iwasawa theory
. \n\nAfter introducing the basic objects (namely\
, the p-adically completed cohomology spaces attac
hed to a given reductive group)\, I will explain s
everal key conjectures that we expect to hold\, in
cluding the conjectural relationship to Galois def
ormation spaces. Although these conjectures seem o
ut of reach at present in general\, some progress
has been made towards them in particular cases. I
will describe some of this progress\, and along th
e way will introduce some of the tools that we hav
e developed for studying p-adically completed coho
mology\, the most important of these being the Poi
ncare duality spectral sequence. \n\nThis is joint
work with Frank Calegari.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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