{"paper":{"title":"Carlsson's Conjecture and the Generalized Total Rank Conjecture in Characteristic Two","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.RT"],"primary_cat":"math.AC","authors_text":"Keller VandeBogert","submitted_at":"2026-07-24T18:35:29Z","abstract_excerpt":"We prove the generalized total rank conjecture over regular rings in characteristic $2$: if $R$ is\n  a regular Noetherian\n  domain of characteristic $2$ and $P$ is a differential $R$-module admitting a finite projective\n  flag and having nonzero homology $H(P)$, then $\\rank_R(P)\\ge2^{\\codim_RH(P)}$. In particular, we\n  prove Carlsson's conjecture for elementary abelian $2$-groups in every rank. We also\n  obtain sharp homology bounds for arbitrary continuous actions of such groups and for perfect complexes\n  over finite group algebras; the sphere rank conjecture follows. The proof identifies th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.22844","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.22844/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"}