Let F be a finite extension of. Let be the Drinfeld upper half plane, and the first Drinfeld covering of. We study the affinoid open subset of above a vertex of the Bruhat-Tits tree for. Our main result is that, which we establish by showing that for the Deligne-Lusztig variety of. One formal consequence is a description of the representation of as the p-adic completion of.
The Picard group of vertex affinoids in the first Drinfeld covering
Taylor J.
2023
Abstract
Let F be a finite extension of. Let be the Drinfeld upper half plane, and the first Drinfeld covering of. We study the affinoid open subset of above a vertex of the Bruhat-Tits tree for. Our main result is that, which we establish by showing that for the Deligne-Lusztig variety of. One formal consequence is a description of the representation of as the p-adic completion of.
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