Séminaires : Séminaire Groupes Réductifs et Formes Automorphes

Equipe(s) : fa, tn,
Responsables :Alexis Bouthier, Francesco Lemma
Email des responsables : alexis.bouthier@imj-prg.fr, francesco.lemma(at)imj-prg.fr
Salle :
Adresse :

Orateur(s) Hans-Jürgen SCHNEIDER - ,
Titre Iwahori-Hecke algebras are Gorenstein
Horaire10:30 à 11:30
RésumeLet $G$ be a split connected reductive group over a finite extension of $Q_p$, and let $H$ be the (pro-$p$) Iwahori-Hecke algebra of $G$ with coefficients in an arbitrary field $k$. In the classical case, where $k$ has characteristic zero, $H$ is known, by Bernstein, to be a regular ring. This means that any $H$-module has a finite projective resolution. This is no longer the case if $k$ has characteristic $p$. In joint work with R. Ollivier we prove that $H$ always is a Gorenstein ring, i.e., has finite injective dimension as a module over itself.