@article{18154,
  abstract     = {In 1976, Deligne and Lusztig realized the representation theory of finite groups of Lie type inside étale cohomology of certain algebraic varieties. Recently, a p-adic version of this theory started to emerge: there are p-adic Deligne–Lusztig spaces, whose cohomology encodes representation theoretic information for p-adic groups – for instance, it partially realizes the local Langlands correspondence with characteristic zero coefficients. However, the parallel case of coefficients of positive characteristic  ℓ≠p has not been inspected so far. The purpose of this article is to initiate such an inspection. In particular, we relate cohomology of certain p-adic Deligne–Lusztig spaces to Vignéras's modular local Langlands correspondence for GLn.},
  author       = {Löwit, Jakub},
  issn         = {1090-266X},
  journal      = {Journal of Algebra},
  number       = {2},
  pages        = {81--118},
  publisher    = {Elsevier},
  title        = {{On modulo ℓ cohomology of p-adic Deligne–Lusztig varieties for GLn}},
  doi          = {10.1016/j.jalgebra.2024.08.033},
  volume       = {663},
  year         = {2025},
}