{"paper":{"title":"Bia{\\l}ynicki-Birula decomposition for reductive groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Joachim Jelisiejew, {\\L}ukasz Sienkiewicz","submitted_at":"2018-05-29T16:07:57Z","abstract_excerpt":"We generalize the Bia{\\l}ynicki-Birula decomposition from actions of $G_m$ on smooth varieties to actions of linearly reductive group ${\\bf G}$ on finite type schemes and algebraic spaces. We also provide a relative version and briefly discuss the case of algebraic stacks.\n  We define the Bia{\\l}ynicki-Birula decomposition functorially: for a fixed ${\\bf G}$-scheme $X$ and a monoid $\\overline{\\bf G}$ which partially compactifies ${\\bf G}$, the BB decomposition parameterizes ${\\bf G}$-schemes over $X$ for which the ${\\bf G}$-action extends to the $\\overline{\\bf G}$-action. The freedom of choice"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.11558","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"}