{"paper":{"title":"The modular pro-$p$ Iwahori-Hecke ${\\operatorname{Ext}}$-algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.RT","authors_text":"Peter Schneider, Rachel Ollivier","submitted_at":"2018-08-28T19:15:58Z","abstract_excerpt":"Let $\\mathfrak F$ be a locally compact nonarchimedean field of positive residue characteristic $p$ and $k$ a field of characteristic $p$. Let $G$ be the group of $\\mathfrak{F}$-rational points of a connected reductive group over $\\mathfrak{F}$ which we suppose $\\mathfrak F$-split. Given a pro-$p$ Iwahori subgroup $I$ of $G$, we consider the space $\\mathbf X$ of $k$-valued functions with compact support on $G/I$. It is naturally an object in the category ${\\operatorname{Mod}}{(G)}$ of all smooth $k$-representations of $G$.\n  We study the graded Ext-algebra $E^*={\\operatorname{Ext}}_{{\\operatorn"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.09503","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}