{"paper":{"title":"Mixed Motives and Geometric Representation Theory in Equal Characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.KT"],"primary_cat":"math.RT","authors_text":"Jens Niklas Eberhardt, Shane Kelly","submitted_at":"2016-09-19T22:13:05Z","abstract_excerpt":"Let $\\mathbb{k}$ be a field of characteristic $p$. We introduce a formalism of mixed sheaves with coefficients in $\\mathbb{k}$ and showcase its use in representation theory. More precisely, we construct for all quasi-projective schemes $X$ over an algebraic closure of $\\mathbb{F}_p$ a $\\mathbb{k}$-linear triangulated category of motives on $X$. Using work of Ayoub (2007), Cisinski-Deglise (2012) and Geisser-Levine (2000), we show that this system of categories has a six functors formalism and computes higher Chow groups. Indeed, it behaves similarly to other categories of sheaves that one is u"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.05956","kind":"arxiv","version":2},"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"}