@PhdThesis{duepublico_mods_00081953, author = {Gaillard, Virginie}, title = {Modular representation theory and sheaves on the Bruhat--Tits building}, year = {2024}, month = {May}, day = {13}, abstract = {Let {\$}G{\$} denote the group of rational points of a split connected reductive group over a nonarchimedean local field. Furthermore, let {\$}R{\$} denote a quasi-Frobenius ring and let {\$}H{\$} denote the pro-{\$}p{\$} Iwahori-Hecke algebra of {\$}G{\$} over {\$}R{\$}. Inspired by the work of Schneider and Stuhler, Schneider, and Kohlhaase we construct a fully faithful functor from the category of {\$}H{\$}-modules into that of {\$}G{\$}-equivariant sheaves of {\$}R{\$}-modules on the Bruhat-Tits building {\$}{\backslash}mathscr{\{}X{\}}{\$} of {\$}G{\$}. We study the cohomology (with compact support) of our sheaves in terms of the homology of {\$}G{\$}-equivariant coefficient systems, using Verdier duality on the building.}, doi = {10.17185/duepublico/81953}, url = {https://duepublico2.uni-due.de/receive/duepublico_mods_00081953}, url = {https://doi.org/10.17185/duepublico/81953}, file = {:https://duepublico2.uni-due.de/servlets/MCRFileNodeServlet/duepublico_derivate_00081468/Diss_Gaillard.pdf:PDF}, language = {en} }