| 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 étale $(\varphi, \Gamma)$- modules attached to the coefficients. |