{"paper":{"title":"Geometric and homological properties of affine Deligne-Lusztig varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Xuhua He","submitted_at":"2012-01-24T00:57:02Z","abstract_excerpt":"This paper studies affine Deligne-Lusztig varieties $X_{\\tw}(b)$ in the affine flag variety of a quasi-split tamely ramified group. We describe the geometric structure of $X_{\\tw}(b)$ for a minimal length element $\\tw$ in the conjugacy class of an extended affine Weyl group, generalizing one of the main results in \\cite{HL} to the affine case. We then provide a reduction method that relates the structure of $X_{\\tw}(b)$ for arbitrary elements $\\tw$ in the extended affine Weyl group to those associated with minimal length elements. Based on this reduction, we establish a connection between the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.4901","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"}