8 papers
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…
Nearby cycles commute with proper direct image on stacks of shtukas
Arnaud Eteve, Cong Xue
Let be a generically reductive group over a smooth projective curve over a finite field. For any finite set , we show that nearby cycles commute with proper direct image…
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…