TY  - GEN
AV  - public
TI  - Analytic cohomology of families of L-analytic Lubin-Tate (?_L,?_L)-modules
N2  - In this thesis we prove finiteness and base change properties for analytic cohomology
of families of L-analytic (?_L, ?_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 (?_L, ?_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 ?_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.
A1  - Steingart, Rustam
CY  - Heidelberg
UR  - https://archiv.ub.uni-heidelberg.de/volltextserver/32192/
Y1  - 2022///
ID  - heidok32192
ER  -