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UID:6065@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20220502T140000
DTEND;TZID=Europe/Paris:20220502T150000
DTSTAMP:20241120T200905Z
URL:https://www.i2m.univ-amu.fr/evenements/graded-hecke-algebras-and-equiv
 ariant-sheaves-in-the-local-langlands-program/
SUMMARY:Maarten Solleveld (Radboud Universiteit Nijmegen\, The Netherlands)
 : Graded Hecke algebras and equivariant sheaves in the local Langlands pro
 gram
DESCRIPTION:Maarten Solleveld: It has been conjectured that the local Langl
 ands correspondence for a reductive p-adic group G (itself also partly con
 jectural) can be categorified. Then it should relate the category of compl
 ex smooth G-representations with a category of equivariant sheaves on a va
 riety of Langlands parameters for G. If it exists\, such a categorificatio
 n will probably arise via Hecke algebras.\nIn this talk we will discuss se
 veral steps in this direction. Our main players will be graded Hecke algeb
 ras\, which appear both on the p-adic side and on the Galois side of the l
 ocal Langlands program. We will see that graded Hecke algebras can not onl
 y be constructed in terms of generators and relations\, but also geometric
 ally\, as endomorphism algebras of certain equivariant constructible sheav
 es. That leads to to geometric constructions of irreducible Hecke algebra 
 modules and to comparison theorems between derived categories of equivaria
 nt sheaves and derived module categories of graded Hecke algebras.\nWe can
  apply these Hecke algebras techniques in the local Langlands program\, co
 njecturally for all reductive p-adic groups and certainly for some well-kn
 own groups. That provides a description of derived categories of equivaria
 nt constructible sheaves on suitable varieties of Langlands parameters.\n
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 022/04/Maarten_Solleveld.png
CATEGORIES:Séminaire,Représentations des Groupes Réductifs,Virtual
 event
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