Compairing Categories of Lubin–Tate $$(\varphi _L,\Gamma _L)$$-Modules

Abstract

In the Lubin–Tate setting we compare different categories of $$(\varphi _L,\Gamma )$$ ( φ L , Γ ) -modules over various perfect or imperfect coefficient rings. Moreover, we study their associated Herr-complexes. Finally, we show that a Lubin Tate extension gives rise to a weakly decompleting, but not decompleting tower in the sense of Kedlaya and Liu.