Arnaud Eteve

Welcome to my webpage ! 

I am currently a postdoctoral fellow at the Max Planck Institute for Mathematics in Bonn in the research group of Jessica Fintzen. 

Before I was doing my Phd in Paris under the direction of Jean-François Dat . Here are some subjects I am interested in  : 

• Langlands program : local and global both arithmetic and geometric

• Representations of finite and p-adic Lie groups : Deligne-Lusztig theory, modular aspects, type theory, ... 

• Hecke categories, geometric Satake, Bezrukavnikov equivalences, Soergel bimodules, character sheaves, ... 

• Categorical traces and categorification

• Stacks of chtoucas : their geometry and their cohomology

Research

• Kazhdan-Laumon sheaves and Deligne-Lusztig representations, 2023, arxiv link 

• Universal Koszul duality for Kac-Moody groups, with Jens Eberhardt, 2024, arxiv link, journal link, Compositio Mathematica, 162 (2026), no. 5, 1053–1092 

• Nearby cycles commutes with proper direct image on stacks of shtukas, with Cong Xue, 2024, arxiv link, journal link , Advances in Mathematics, 485 (2026)

• Free monodromic Hecke categories and their categorical traces, 2024, arxiv link, submitted

• Tilting representations of finite groups of Lie type, 2024, arxiv link, submitted

• The parabolic K-motivic Hecke category, with Jens Eberhardt, 2025, arxiv link, submitted

• Application of the trace formalism to Deligne-Lusztig theory, 2025, arxiv link, improved V2 in preparation

• The extended Fargues-Scholze spectral action, with Peter Dillery, 2026, arxiv link

• Spectral action on isocrystals (title to be changed), with Dennis Gaitsgory, Alain Genestier and Vincent Lafforgue, in preparation, 

  • Oberwolfach Report on this paper, 54/2024, link

• Introduction to categorical traces, in preparation for the Proceedings of the 'Categorical Langlands summit', videos available on youtube : part 1, part 2, part 3

• My thesis, Monodromic sheaves, Deligne-Lusztig theory and depth 0 cohomology of stacks of chtoucas, link

Teaching

• Winter semester, 2024, Introduction to Deligne-Lusztig theory. 

• 2020-2023, Teaching assistant for the commutative algebra course 'Algèbre 2' at Ecole Normale Supérieure