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Abstract

In this thesis we prove finiteness and base change properties for analytic cohomology of families of L-analytic (φ_L, Γ_L)-modules parametrised by affinoid algebras. To this end, we study an analogue of the Herr complex, which can be defined using p-adic Fourier theory. For technical reasons we work over a field containing the finite ex- tension L of Q_p and a certain transcendental period. In case the affinoid algebra is the base field, we prove that coadmissibility of the Iwa- sawa cohomology groups is sufficient for the existence of a comparison isomorphism between the Iwasawa cohomology of a (φ_L, Γ_L )-module over the Robba ring and the analytic cohomology of its Lubin-Tate deformation, which, roughly speaking, is ob- tained by base change to the algebra of L-analytic distributions on an open subgroup of Γ_L . In the trianguline case we show that the complex computing Iwasawa cohomology is perfect and in particular satisfies the above condition. Finally we describe how general perfectness results for Iwasawa cohomology can be achieved assuming conjecturally that the statement can be proved in the étale case.