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SUMMARY:Andrea Dotto (Univ. of Chicago)
DTSTART:20201117T210000Z
DTEND:20201117T220000Z
DTSTAMP:20260423T041505Z
UID:UAANTS/7
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UAANTS/7/">M
 od p Bernstein centres of p-adic groups</a>\nby Andrea Dotto (Univ. of Chi
 cago) as part of University of Arizona Algebra and Number Theory Seminar\n
 \n\nAbstract\nThe centre of the category of smooth mod p representations o
 f a p-adic reductive group does not distinguish the blocks of finite lengt
 h representations\, in contrast with Bernstein's theory in characteristic 
 zero. Motivated by this observaton and the known connections between the B
 ernstein centre and the local Langlands correspondence in families\, we co
 nsider the case of GL_2(Q_p) and we prove that its category of representat
 ions extends to a stack on the Zariski site of a simple geometric object: 
 a chain X of projective lines\, whose points are in bijection with Paskuna
 s's blocks. Taking the centre over each open subset we obtain a sheaf of r
 ings on X\, and we expect the resulting space to be closely related to the
  Emerton--Gee stack for 2-dimensional representations of the absolute Galo
 is group of Q_p. Joint work in progress with Matthew Emerton and Toby Gee.
 \n
LOCATION:https://researchseminars.org/talk/UAANTS/7/
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