We develop an extension of Deligne--Lusztig theory to certain (possibly infinite type) disconnected reductive groups arising from the special fibers of point stabilizers in the Bruhat--Tits building, which we call \emph{paraductive}. We then compute explicit lower bounds for the Tate cohomology of representations of paraductive groups, relating these to Shintani descent, Lusztig restriction, and the Glauberman correspondence. As an application, using Feng's modular functoriality and Scholze's independence of $\ell$, we compute the Fargues--Scholze L-parameters of non-singular depth $0$ cuspidal representations of a (possibly wildly ramified) reductive group over a nonarchimedean local field.
Let $G$ be a quasi-split reductive group over a finite field and let $\^G$ be the Langlands dual group. Assuming the derived subgroup of $G$ is almost simple, we use techniques from the geometric Langlands program to relate special values of Bessel functions for generic principal series representations of $G$ to the tr...
We study constructible $\mathbb{Z}[\tfrac{1}{p}]$-linear \'etale motives on parahoric Hecke stacks associated with quasi-split tamely ramified reductive groups. We prove a canonical equivalence between their equal-characteristic and Witt-vector incarnations that is monoidal with respect to convolution. This extends Ban...
We generalise Yin's motivic integration with section to the Hensel-minimal framework, with and without volume forms, building on Stout and Vermeulen's work on a Hrushovski-Kazhdan style motivic integral for $1$-h-minimal valued fields. In particular, we get a bijective motivic integral \emph{\`a la} Hrushovski-Kazhdan...
We compute an explicit contribution of supercuspidal representations arising from Yu's construction to the middle \'etale cohomology of local Shimura varieties. For the proof, we construct special affinoids in local Shimura varieties whose reductions are isomorphic to Heisenberg Deligne-Lusztig varieties and then apply...
We give a desingularization-free proof of Voevodsky's identification of bistable mod-$\ell$ motivic cohomology operations with the motivic Steenrod algebra over fields of characteristic zero. This supplies the direct argument anticipated by Voevodsky in his study of motivic Eilenberg--MacLane spaces. As an application,...
Jia-Hao Hu· 0 citations
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