{"paper":{"title":"Components of affine Springer fibers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RT","authors_text":"Cheng-Chiang Tsai","submitted_at":"2016-09-16T18:58:34Z","abstract_excerpt":"Let $\\mathbf{G}$ be a connected split reductive group over a field of characteristic zero or sufficiently large characteristic, $\\gamma_0\\in(\\operatorname{Lie}\\mathbf{G})((t))$ be any topologically nilpotent regular semisimple element, and $\\gamma=t\\gamma_0$. Using methods from $p$-adic orbital integrals, we show that the number of components of the Iwahori affine Springer fiber over $\\gamma$ modulo $Z_{\\mathbf{G}((t))}(\\gamma)$ is equal to the order of the Weyl group."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.05176","kind":"arxiv","version":3},"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"}