A Tannakian description of the local Kaletha gerbe

Alexander Bertoloni Meli; Peter Dillery

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arXiv · 2601.07042

A Tannakian description of the local Kaletha gerbe

Alexander Bertoloni Meli·Peter Dillery

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Abstract

We construct, for a $p$-adic field $F$, an explicit semisimple Tannakian category $\text{RigIsoc}_{F}$ whose category of fiber functors recovers Kaletha's Galois gerbe $\mathcal{E}_{\text{Kal}}$. We then classify and write down the simple objects in $\text{RigIsoc}_{F}$, all of which come from elliptic twisted Levi subgroups of $\mathrm{GL}_{n}$.

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Alexander Bertoloni Meli, Peter Dillery. 2026-01-11. A Tannakian description of the local Kaletha gerbe. https://arxiv.org/abs/2601.07042

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