Abstract:We formulate Schneider--Teitelbaum duality between wide classes of Banach $k$-linear representations of $G$ and left $O_k[[G]]$-modules for a non-spherically complete field $k$, e.g.\ $\mathbb{C}_p$, and a profinite group $G$. We interpret a topological notion of a weak variant of irreducibility of a Banach $k$-linear representation of $G$ into a purely algebraic notion of a certain simplicity of the dual left $O_k[[G]]$-module. As applications, we give two $p$-adic families of infinite dimensional Banach $\mathbb{C}_p$-linear representations of a $p$-adic Lie group satisfying the weak irreducibility.
From: Tomoki Mihara [view email]
[v1]
Wed, 17 Jun 2026 12:25:55 UTC (30 KB)
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