Functor Homology Over an Additive Category

Aurélien Djament, Antoine Touzé

Published 2021-11-18Version 1

We prove a series of results which open the way to computations of functor homology over arbitary additive categories. In particular, we generalize the strong comparison theorem of Franjou Friedlander Scorichenko and Suslin to an arbitrary Fp-linear additive category. This result allows us to compare the cohomology of the classical algebraic groups and the cohomology of their discrete groups of k-points when k is an infinite perfect field of positive characteristic, in the spirit of the celebrated theorem of Cline Parshall Scott and van der Kallen over finite fields.