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SUMMARY:A homotopical approach to smooth mod-p representation theory - Nic
 olas Dupré\, University of Duisburg-Essen
DTSTART:20240529T153000Z
DTEND:20240529T163000Z
UID:TALK216340@talks.cam.ac.uk
CONTACT:Adam Jones
DESCRIPTION:Let k be a field of characteristic p>0 and let G be a topologi
 cal group admitting an open pro-p subgroup. If H=k[I\\G/I] denotes the cor
 responding Hecke algebra\, then the functor of taking I-invariants provide
 s an adjunction between the category of smooth k-linear representations of
  G and the category of H-modules. When H is the pro-p Iwahori-Hecke algebr
 a of a p-adic reductive group\, this adjunction is not well-understood. Th
 is is one of the main obstacles to understanding the smooth representation
  theory of these groups and to the mod-p Langlands program. I will describ
 e a recent approach to studying this adjunction using the language and tec
 hniques from the theory of model categories. I will then finish by describ
 ing the homotopy classes of simple supersingular pro-p Iwahori-Hecke modul
 es for GL_n.This is joint work with Jan Kohlhaase\n
LOCATION:MR12
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