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SUMMARY:Modular Iwahori-Hecke algebras: A survey and some computations
DTSTART;VALUE=DATE-TIME:20160308T090000Z
DTEND;VALUE=DATE-TIME:20160308T100000Z
DTSTAMP;VALUE=DATE-TIME:20190618T153118Z
UID:indico-event-1100@indico.math.cnrs.fr
DESCRIPTION:\nAvec le soutien de :\n\n\n \n\nERC Advanced Grant : AAMOT
(Arithmetic of Automorphic Motives)\n\n \n\nPI : Michael HARRIS\n\n\n\nT
he smooth representation theory of a p-adic reductive group G with charact
eristic zero coefficients is very closely connected to the module theory o
f its (pro-p) Iwahori-Hecke algebra H = H(G). In the modular case\,where t
he coefficients have characteristic p\, this connection breaks down to a l
arge extent. In this talk I will first survey joint work with R. Ollivier
in this modular case. \n\nWe determine completely the homological propert
ies of H\, and we introduce a certain torsion theory in the module categor
y Mod(H) such that the torsion free modules embed fully faithfully into th
e category of smooth G-representations. In the case of the group SL_
2 we are able to explicitly compute this torsion theory. Secondly I will d
escribe a derived picture of the whole situation in which one recovers an
equivalence between the module theory of a derived version of H and the
derived representation theory of G. In both approaches the cohomology of
the pro-p Iwahori subgroup of G in a certain universal module plays a cru
cial role.\n\nhttps://indico.math.cnrs.fr/event/1100/
LOCATION:IHES Amphithéâtre Léon Motchane
URL:https://indico.math.cnrs.fr/event/1100/
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