MODEL CATEGORIES AND PRO-<i>p</i> IWAHORI–HECKE MODULES

Abstract Let G denote a possibly discrete topological group admitting an open subgroup I which is pro- p . If H denotes the corresponding Hecke algebra over field k of characteristic , then we study adjunction between -modules and -linear smooth -representations in terms various model structures. Gorenstein ring, single out full subcategory equivalent to category all projective via functor -invariants. This applies groups rational points split connected reductive finite non-Archimedean local fields, thus generalizing theorem Cabanes. Moreover, show that structure on admits right transfer. On homotopy level, derived -invariants inverse becomes equivalence when restricted suitable subcategory.