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SUMMARY:The Derived l-modular Unipotent Block of p-adic GLn [Oberseminar D
 arstellungstheorie]
DTSTART:20251024T121500Z
DTEND:20251024T131500Z
DTSTAMP:20260308T040100Z
UID:indico-event-818@math-events.uni-bonn.de
DESCRIPTION:Speakers: Rose Berry (MPI Bonn)\n\nThe theory of smooth repres
 entations of reductive groups overp-adic fields appears on one side of the
  local Langlands correspondence\,which relates it to representations assoc
 iated to the absolute Galoisgroup of the p-adic field. With coefficients i
 n the complex numbers\, thedecomposition of Bernstein describes the blocks
  of the category ofrepresentations\, and in many cases the theory of types
  gives anequivalence between each block and the category of modules over a
 nexplicit Hecke algebra. When we generalise the coefficients toalgebraical
 ly closed fields of characteristic l not equal to p\, all ofthis can fail.
  Bernstein's decomposition fails for most groups\, thoughit still holds fo
 r GLn. However\, even in this case\, the equivalence witha Hecke algebra f
 ails\, though partial results are still known\, involvinginstead a Schur a
 lgebra. Building on these\, I give an equivalencebetween a derived categor
 y of the unipotent block (the block containingthe trivial representation) 
 and perfect complexes over a dg-enrichedSchur algebra.\n\nhttps://math-eve
 nts.uni-bonn.de/event/818/
LOCATION:Endenicher Allee 60/1.008 - Seminarraum (Mathezentrum)
URL:https://math-events.uni-bonn.de/event/818/
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