Appears in collection : Reductive groups and automorphic forms. Dedicated to the French school of automorphic forms and in memory of Roger Godement.

In the modular smooth representation theory of p-adic reductive groups with coefficents in a field of characteristic p (same p!) a close relation between smooth representations and modules over suitable Hecke algebras only holds in a derived version. This leads to differential graded Hecke algebras and their Ext(= cohomology)-algebras. I will report on joint work with R. Ollivier on the structural properties of the pro-p Iwahori Ext-algebra. If time permits I will also discuss the formalism of derived parabolic induction (joint work with S. Scherotzke)