title: Analytic cohomology of families of L-analytic Lubin-Tate (φ_L,Γ_L)-modules
creator: Steingart, Rustam
subject: ddc-510
subject: 510 Mathematics
description: 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.
date: 2022
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/32192/1/DissertationRustamSteingartMitErrata.pdf
identifier: DOI:10.11588/heidok.00032192
identifier: urn:nbn:de:bsz:16-heidok-321929
identifier:   Steingart, Rustam  (2022) Analytic cohomology of families of L-analytic Lubin-Tate (φ_L,Γ_L)-modules.  [Dissertation]     
relation: https://archiv.ub.uni-heidelberg.de/volltextserver/32192/
rights: info:eu-repo/semantics/openAccess
rights: http://archiv.ub.uni-heidelberg.de/volltextserver/help/license_urhg.html
language: eng