Finiteness of analytic cohomology of Lubin-Tate $({\phi }_L,{\Gamma }_L)$-modules

Abstract

We prove finiteness and base change properties for analytic cohomology of families of $L$-analytic $({\phi }_L,{\Gamma }_L)$-modules parametrised by affinoid algebras in the sense of Tate. For technical reasons we work over a field $K$ containing a period of the Lubin-Tate group, which allows us to describe analytic cohomology in terms of an explicit generalized Herr complex.

Updated numbering and added DOI of the published version

References in corpus (1)

• Cohomology of Topologised Monoids

Cited by in corpus (1)

• $\epsilon$-isomorphisms for rank one $(\phi ,\Gamma )$-modules over Lubin-Tate Robba rings