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arXiv · 2606.18999

Schneider--Teitelbaum Duality over a Non-spherically Complete Field

Tomoki Mihara
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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.

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Tomoki Mihara. 2026-06-17. Schneider--Teitelbaum Duality over a Non-spherically Complete Field. https://arxiv.org/abs/2606.18999

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