Smooth representations and Hecke modules in characteristic \(p\) (Q903175)

In this paper, the author works over a field \(k\) of characteristic \(p\) and introduces a differential graded Hecke algebra for the pair \((G,I)\), where \(G\) is a \(p\)-adic Lie group and \(I\subseteq G\) is a compact open subgroup which is a torsion-free pro-\(p\)-group. The main result shows 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 differential graded Hecke algebra.