{"paper":{"title":"Bases of T-equivariant cohomology of Bott-Samelson varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RT","authors_text":"Vladimir Shchigolev","submitted_at":"2016-01-26T19:55:16Z","abstract_excerpt":"We construct combinatorial bases of the $T$-equivariant ($T$ is the maximal torus) cohomology $H^\\bullet_T(\\Sigma,k)$ of the Bott-Samelson variety $\\Sigma$ under some mild restrictions on the field of coefficients $k$. This bases allow us to prove the surjectivity of the restrictions $H^\\bullet_T(\\Sigma,k)\\to H^\\bullet_T(\\pi^{-1}(x),k)$ and $H^\\bullet_T(\\Sigma,k)\\to H^\\bullet_T(\\Sigma\\setminus\\pi^{-1}(x),k)$, where $\\pi:\\Sigma\\to G/B$ is the canonical resolution. In fact, we also construct bases of the targets of these restrictions by picking up certain subsets of certain bases of $H^\\bullet_T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.07146","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"}