title: On Analytic and Iwasawa Cohomology
creator: Thomas, Oliver
subject: 510
subject: 510 Mathematics
description: 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.
date: 2019
type: Dissertation
type: info:eu-repo/semantics/doctoralThesis
type: NonPeerReviewed
format: application/pdf
identifier: https://archiv.ub.uni-heidelberg.de/volltextserverhttps://archiv.ub.uni-heidelberg.de/volltextserver/27443/1/Thomas-OnAnalyticAndIwasawaCohomology.pdf
identifier: DOI:10.11588/heidok.00027443
identifier: urn:nbn:de:bsz:16-heidok-274432
identifier:   Thomas, Oliver  (2019) On Analytic and Iwasawa Cohomology.  [Dissertation]     
relation: https://archiv.ub.uni-heidelberg.de/volltextserver/27443/
rights: info:eu-repo/semantics/openAccess
rights: http://archiv.ub.uni-heidelberg.de/volltextserver/help/license_urhg.html
language: eng