Finiteness of analytic cohomology of Lubin-Tate (φL,ΓL)-modules

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 generalised Herr complex.