article published yes Jakub Löwit author e3b80ae2-eb8e-11eb-b029-9aef4a9108a0 TaHa department 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. https://research-explorer.ista.ac.at/download/18154/18830/2024_JourAlgebra_Loewit.pdf application/pdfno https://creativecommons.org/licenses/by/4.0/ Elsevier2025 eng 0021-8693 1090-266X 2404.11176 00132520780000110.1016/j.jalgebra.2024.08.033 663281-118 Löwit, J. (2025). On modulo ℓ cohomology of p-adic Deligne–Lusztig varieties for GLn. <i>Journal of Algebra</i>. Elsevier. <a href="https://doi.org/10.1016/j.jalgebra.2024.08.033">https://doi.org/10.1016/j.jalgebra.2024.08.033</a> J. Löwit, Journal of Algebra 663 (2025) 81–118. Löwit J. 2025. On modulo ℓ cohomology of p-adic Deligne–Lusztig varieties for GLn. Journal of Algebra. 663(2), 81–118. Löwit J. On modulo ℓ cohomology of p-adic Deligne–Lusztig varieties for GLn. <i>Journal of Algebra</i>. 2025;663(2):81-118. doi:<a href="https://doi.org/10.1016/j.jalgebra.2024.08.033">10.1016/j.jalgebra.2024.08.033</a> J. Löwit, “On modulo ℓ cohomology of p-adic Deligne–Lusztig varieties for GLn,” <i>Journal of Algebra</i>, vol. 663, no. 2. Elsevier, pp. 81–118, 2025. Löwit, Jakub. “On modulo ℓ Cohomology of P-Adic Deligne–Lusztig Varieties for GLn.” <i>Journal of Algebra</i>. Elsevier, 2025. <a href="https://doi.org/10.1016/j.jalgebra.2024.08.033">https://doi.org/10.1016/j.jalgebra.2024.08.033</a>. Löwit, Jakub. “On modulo ℓ Cohomology of P-Adic Deligne–Lusztig Varieties for GLn.” <i>Journal of Algebra</i>, vol. 663, no. 2, Elsevier, 2025, pp. 81–118, doi:<a href="https://doi.org/10.1016/j.jalgebra.2024.08.033">10.1016/j.jalgebra.2024.08.033</a>. 181542024-09-29T22:01:37Z2025-02-27T12:32:40Z