%0 Journal Article
%T Schneider-Teitelbaum duality for locally profinite groups
%J Categories and General Algebraic Structures with Applications
%I Shahid Beheshti University
%Z 2345-5853
%A Mihara, Tomoki
%D 2021
%\ 01/01/2021
%V 14
%N 1
%P 119-166
%! Schneider-Teitelbaum duality for locally profinite groups
%K Iwasawa theory
%K p-adic
%K locally profinite group
%R 10.29252/cgasa.14.1.119
%X We define monoidal structures on several categories of linear topological modules over the valuation ring of a local field, and study module theory with respect to the monoidal structures. We extend the notion of the Iwasawa algebra to a locally profinite group as a monoid with respect to one of the monoidal structure, which does not necessarily form a topological algebra. This is one of the main reasons why we need monoidal structures. We extend Schneider--Teitelbaum duality to duality applicable to a locally profinite group through the module theory over the generalised Iwasawa algebra, and give a criterion of the irreducibility of a unitary Banach representation.
%U https://cgasa.sbu.ac.ir/article_87524_0a893e28ec798a2b4354b71165849781.pdf