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SUMMARY:Benjamin Schraen (Paris-Saclay)
DTSTART:20210624T160000Z
DTEND:20210624T172000Z
DTSTAMP:20260423T021111Z
UID:RAMpAGe/49
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/RAMpAGe/49/"
 >Finite length for cohomological mod p representations of GL2 of a p-adic 
 field</a>\nby Benjamin Schraen (Paris-Saclay) as part of Recent Advances i
 n Modern p-Adic Geometry (RAMpAGe)\n\n\nAbstract\nIn the search for a mod 
 p local Langlands correspondence\, it\nis natural to study the representat
 ions of GL2 of a p-adic field F in\nthe mod p cohomology of Shimura curves
 . It is expected that the action\nof GL2(F) on a Galois-isotypic subspace 
 of the mod p cohomology of a\ntower of Shimura curves (of fixed tame level
 ) has finite length and is\nrelated to the local Galois representation at 
 p. In the case of modular\ncurves\, this is known by the local-global comp
 atibility theorem of\nEmerton. I'll explain how to prove some new cases of
  the finiteness of\nthe length when F is an unramified extension of Qp. Th
 is finiteness is\nrelated to the computation of the Gelfand-Kirillov dimen
 sion of these\nrepresentations. This is a joint work with Christophe Breui
 l\, Florian\nHerzig\, Yongquan Hu and Stefano Morra.\n
LOCATION:https://researchseminars.org/talk/RAMpAGe/49/
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