Smooth representations and Hecke modules in characteristic $p$

Peter Schneider

Vol. 279 (2015), No. 1-2, 447–464

DOI: 10.2140/pjm.2015.279.447

Abstract

Let $G$ be a $p$-adic Lie group and $I\subseteq G$ be a compact open subgroup which is a torsionfree pro-$p$-group. Working over a coefficient field $k$ of characteristic $p$ we introduce a differential graded Hecke algebra for the pair $\left(G,I\right)$ and show that the derived category of smooth representations of $G$ in $k$-vector spaces is naturally equivalent to the derived category of differential graded modules over this Hecke DGA.

Keywords

differential graded Hecke algebra, smooth representation

Mathematical Subject Classification 2010

Primary: 16E45, 20C08, 22E50

Secondary: 16E35

Milestones

Received: 28 May 2015

Accepted: 16 August 2015

Published: 21 December 2015