A Tannakian description of the local Kaletha gerbe
Alexander Bertoloni Meli, Peter Dillery

TL;DR
This paper constructs a Tannakian category over a p-adic field that captures Kaletha's Galois gerbe, providing explicit classification of its simple objects linked to elliptic twisted Levi subgroups.
Contribution
It introduces a new semisimple Tannakian category over p-adic fields that explicitly models Kaletha's Galois gerbe and classifies its simple objects.
Findings
Constructed an explicit semisimple Tannakian category for p-adic fields.
Recovered Kaletha's Galois gerbe via fiber functors.
Classified simple objects related to elliptic twisted Levi subgroups.
Abstract
We construct, for a -adic field , an explicit semisimple Tannakian category whose category of fiber functors recovers Kaletha's Galois gerbe . We then classify and write down the simple objects in , all of which come from elliptic twisted Levi subgroups of .
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Algebraic structures and combinatorial models
