%0 Generic
%A Thomas, Oliver
%C Heidelberg
%D 2019
%F heidok:27443
%R 10.11588/heidok.00027443
%T On Analytic and Iwasawa Cohomology
%U https://archiv.ub.uni-heidelberg.de/volltextserver/27443/
%X We generalise spectral sequences for Iwasawa adjoints of Jannsen to higher dimensional coefficient rings by systematically employing Matlis, local, Koszul and Tate duality. With the same strategy we achieve a generalisation of Venjakob’s local duality theorem for Iwasawa algebras and compute the Λ-torsion of the first Iwasawa cohomology group,both locally and globally. Furthermore, we develop a flexible framework to prove standard results of group cohomology for topologised monoids with coefficients in topologised modules, using explicit methods dating back to Hochschild and Serre. This closes a few argumentative gaps in the literature. We also prove a form of Poincaré duality for Lie groups over arbitrary complete non-archimedean fields of characteristic zero. Finally, we take tentative steps towards applying these results to (φ,Γ)-modules.