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SUMMARY:Andrea Dotto (University of Chicago)
DTSTART:20200624T013000Z
DTEND:20200624T023000Z
DTSTAMP:20260423T024022Z
UID:POINTS/10
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/POINTS/10/">
 Mod p Bernstein centres of p-adic groups</a>\nby Andrea Dotto (University 
 of Chicago) as part of POINTS - Peking Online International Number Theory 
 Seminar\n\n\nAbstract\nThe centre of the category of smooth mod $p$ repres
 entations of a $p$-adic reductive group does not distinguish the blocks of
  finite length representations\, in contrast with Bernstein's theory in ch
 aracteristic zero. Motivated by this observation and the known connections
  between the Bernstein centre and the local Langlands correspondence in fa
 milies\, we consider the case of $\\mathrm{GL}_2(\\mathbb{Q}_p)$ and we pr
 ove that its category of representations extends to a stack on the Zariski
  site of a simple geometric object: a chain $X$ of projective lines\, whos
 e points are in bijection with Paskunas's blocks. Taking the centre over e
 ach open subset we obtain a sheaf of rings on $X$\, and we expect the resu
 lting space to be closely related to the Emerton-Gee stack for $2$-dimensi
 onal representations of the absolute Galois group of $\\mathbb{Q}_p$. Join
 t work in progress with Matthew Emerton and Toby Gee.\n\nZoom ID: 650 3772
  0269\n\nPassword: 585279\n
LOCATION:https://researchseminars.org/talk/POINTS/10/
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