Herr-complexes in the Lubin-Tate setting

TL;DR

This paper generalizes Herr complexes from cyclotomic to Lubin-Tate settings, defining new complexes that compute Galois cohomology for a broader class of $(, )$-modules.

Contribution

It introduces generalized Herr complexes for Lubin-Tate $(, )$-modules, extending prior work to a more general setting.

Findings

Defined generalized $$- and $ $-Herr complexes.

Proved these complexes compute Galois cohomology.

Extended the applicability of Herr complexes to Lubin-Tate modules.

Abstract

In this article we extend work of Herr from the case of cyclotomic $(\varphi,\Gamma)$-modules to the general case of Lubin-Tate $(\varphi,\Gamma)$-modules. In particular, we define generalized $\varphi$- and $\psi$-Herr complexes, which calculate Galois cohomology, when applied to the etale $(\varphi,\Gamma)$-modules attached to the coefficients.