PT Unknown
AU Gaillard, V
TI Modular representation theory and sheaves on the Bruhat--Tits building
PD 05
PY 2024
DI 10.17185/duepublico/81953
LA en
AB Let $G$ denote the group of rational points of a split connected reductive group over a nonarchimedean local field. Furthermore, let $R$ denote a quasi-Frobenius ring and let $H$ denote the pro-$p$ Iwahori-Hecke algebra of $G$ over $R$. Inspired by the work of Schneider and Stuhler, Schneider, and Kohlhaase we construct a fully faithful functor from the category of $H$-modules into that of $G$-equivariant sheaves of $R$-modules on the Bruhat-Tits building $\mathscr{X}$ of $G$. We study the cohomology (with compact support) of our sheaves in terms of the homology of $G$-equivariant coefficient systems, using Verdier duality on the building.
ER