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CATEGORIES:Junior Algebra and Number Theory seminar
SUMMARY:Smooth representations\, projective resolutions an
d cosheaves - Katerina Hristova\, University of Wa
rwick
DTSTART;TZID=Europe/London:20171124T150000
DTEND;TZID=Europe/London:20171124T160000
UID:TALK86491AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/86491
DESCRIPTION:For a locally compact totally disconnected topolog
ical group G one can define a ‘smooth’ representat
ion. This is just a representation with an extra c
ontinuity condition. The category of all such repr
esentations is abelian\, Noetherian and has enough
projectives. In particular\, one can study its pr
ojective dimension. In this talk we explain how to
put a bound on the projective dimension of this c
ategory and moreover we show how to explicitly con
struct a projective resolution for each smooth G-m
odule. The construction is inspired by a Theorem o
f Bernstein\, who shows how this is done in the ca
se of reductive p-adic groups. We generalise his a
pproach to the case of an arbitrary locally compac
t totally disconnected group. However\, the resolu
tions which Bernstein constructs are not of finite
ly generated projective modules. In the second par
t of the talk\, following the work of Peter Schnei
der and Ulrich Stuhler for reductive algebraic gro
ups\, we explain how to construct finitely generat
ed resolutions by passing to a category of G-equiv
ariant objects\, more precisely - a category of co
sheaves on a simplicial complex on which G acts. T
hroughout we give examples of all our construction
s for SL_n(Q_p) and GL_n(Q_p).
LOCATION:CMS\, MR14
CONTACT:Nicolas Dupré
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