{"paper":{"title":"Equivalences of tame blocks for p-adic linear groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Jean-Fran\\c{c}ois Dat (IMJ)","submitted_at":"2016-03-23T15:12:41Z","abstract_excerpt":"Let p and $\\ell$ be two distinct primes, F a p-adic field and n an integer. We show that any level 0 block of the category of smooth Z $\\ell$-valued representations of GL n (F) is equivalent to the unipotent block of an appropriate product of GL n i (F i). To this end, we first show that the level 0 category of GL n (F) is equivalent to a category of \" modules \" over a certain Z $\\ell$-algebra \" with many objects \" whose definition only involves n and the residue field of F. Then we use fine properties of Deligne-Lusztig cohomology to split this algebra and produce suitable Morita equivalences"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07226","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"}