Compairing categories of Lubin-Tate $(\varphi_L,\Gamma_L)$-modules

TL;DR

This paper compares different categories of Lubin-Tate $(L,G)$-modules over various rings, studies their Herr-complexes, and analyzes the properties of Lubin Tate extensions in relation to decompleting towers.

Contribution

It introduces a comparison of categories of $(L,G)$-modules over different rings and examines their Herr-complexes, also characterizing Lubin Tate extensions as weakly decompleting towers.

Findings

Lubin Tate extensions form weakly decompleting towers

Comparison of categories over perfect and imperfect rings

Analysis of Herr-complexes associated with these modules

Abstract

In the Lubin-Tate setting we compare different categories of $(\varphi_L,\Gamma_L)$-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.