{"paper":{"title":"A lower bound on the essential dimension of $\\operatorname{\\mathbf{PGL}}_{4}$ in characteristic $2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Sanghoon Baek","submitted_at":"2014-11-22T07:01:11Z","abstract_excerpt":"In the present paper, we provide a lower bound of the essential dimension over a field of positive characteristic via Kato's cohomology group, defined by cokernel of a general Artin-Schreier operator. Combining this with Tignol's result on the second trace form of simple algebras of degree $4$, we show that $\\operatorname{ed}(\\operatorname{\\mathbf{PGL}}_{4})\\geq 4$ over a field of characteristic $2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.6089","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"}