{"paper":{"title":"The Orlik-Solomon Algebra and the Bergman Fan of a Matroid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AG","authors_text":"Ilia Zharkov","submitted_at":"2012-09-07T21:12:11Z","abstract_excerpt":"Given a matroid $M$ one can define its Orlik-Solomon algebra $OS(M)$ and the Bergman fan $\\Sigma_0(M)$. On the other hand to any rational polyhedral fan $\\Sigma$ one can associate its tropical homology and cohomology groups $\\F_\\bullet(\\Sigma)$, $\\F^\\bullet (\\Sigma)$. We will show that the projective Orlik-Solomon algebra $OS_0(M)$ is canonically isomorphic to $\\F^\\bullet (\\Sigma_0(M))$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.1651","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"}