7 papers · 1 filter
The extended Fargues--Scholze spectral action
Peter Dillery, Arnaud Eteve
Let be a connected reductive group over a non-archimedean local field. The main result of Fargues and Scholze [FS21] for the geometrization of the local Langlands correspondenc…
The Parabolic K-motivic Hecke Category
Jens Niklas Eberhardt, Arnaud Eteve
We define and study the parabolic K-motivic Hecke category of a (possibly disconnected) Kac-Moody group. Our main result is a combinatorial description via singular K-theory Soerge…
Jordan decomposition, categorical traces and Deligne-Lusztig theory
Arnaud Eteve
This paper is a continuation of the author's previous work. We use the categorical trace formalism to construct a categorical Jordan decomposition for representations of finite gro…
Tilting representations of finite groups of Lie type
Arnaud Eteve
Let be a connected reductive group over a finite field of characteristic . In this paper, we study a category which we call Deligne--Lusztig cate…
Free monodromic Hecke categories and their categorical traces
Arnaud Eteve
The goal of this paper is to give a new construction of the free monodromic categories defined by Yun. We then use this formalism to give simpler constructions of the free monodrom…
Universal Koszul Duality for Kac-Moody Groups
Jens Niklas Eberhardt, Arnaud Eteve
We prove a monoidal equivalence, called universal Koszul duality, between genuine equivariant K-motives on a Kac-Moody flag variety and constructible monodromic sheaves on its Lang…
Kazhdan-Laumon sheaves and Deligne-Lusztig representations
Arnaud Eteve
Let be a reductive group over a finite field with a maximal unipotent subgroup , we consider certain sheaves on defined by Kazhdan and Laumon and show that their cohom…