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SUMMARY:Smooth representations\, projective resolutions and cosheaves - Ka
 terina Hristova\, University of Warwick
DTSTART:20171124T150000Z
DTEND:20171124T160000Z
UID:TALK86491@talks.cam.ac.uk
CONTACT:Nicolas Dupré
DESCRIPTION:For a locally compact totally disconnected topological group G
  one can define a ‘smooth’ representation. This is just a representati
 on with an extra continuity condition. The category of all such representa
 tions is abelian\, Noetherian and has enough projectives. In particular\, 
 one can study its projective dimension. In this talk we explain how to put
  a bound on the projective dimension of this category and moreover we show
  how to explicitly construct a projective resolution for each smooth G-mod
 ule. The construction is inspired by a Theorem of Bernstein\, who shows ho
 w this is done in the case of reductive p-adic groups. We generalise his a
 pproach to the case of an arbitrary locally compact totally disconnected g
 roup. However\, the resolutions which Bernstein constructs are not of fini
 tely generated projective modules. In the second part of the talk\, follow
 ing the work of Peter Schneider and Ulrich Stuhler for reductive algebraic
  groups\, we explain how to construct finitely generated resolutions by pa
 ssing to a category of G-equivariant objects\, more precisely - a category
  of cosheaves on a simplicial complex on which G acts. Throughout we give 
 examples of all our constructions for SL_n(Q_p) and GL_n(Q_p).
LOCATION:CMS\, MR14
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