Herr-complexes in the Lubin-Tate setting

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.