{"paper":{"title":"The Negation Of Singer's Conjecture For The Sixth Algebraic Transfer","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA","math.RT"],"primary_cat":"math.AT","authors_text":"Dang Vo Phuc","submitted_at":"2025-09-11T13:40:40Z","abstract_excerpt":"Let $\\mathscr A$ be the Steenrod algebra over the field of characteristic two, $\\mathbb F_2.$ Denote by $GL(q)$ the general linear group of rank $q$ over $\\mathbb F_2.$ The algebraic transfer, introduced by W. Singer [Math. Z. 202 (1989), 493-523], is a rather effective tool for unraveling the intricate structure of the (mod-2) cohomology of the Steenrod algebra, ${\\rm Ext}_{\\mathscr A}^{q,*}(\\mathbb F_2, \\mathbb F_2).$ The Kameko homomorphism is one of the useful tools to study the dimension of the domain of the Singer transfer. Singer conjectured that the algebraic transfer is always a monom"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.09455","kind":"arxiv","version":8},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2509.09455/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}