{"paper":{"title":"Quotient stacks and equivariant \\'etale cohomology algebras: Quillen's theory revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Luc Illusie, Weizhe Zheng","submitted_at":"2013-05-02T08:16:38Z","abstract_excerpt":"Let $k$ be an algebraically closed field. Let $\\Lambda$ be a noetherian commutative ring annihilated by an integer invertible in $k$ and let $\\ell$ be a prime number different from the characteristic of $k$. We prove that if $X$ is a separated algebraic space of finite type over $k$ endowed with an action of a $k$-algebraic group $G$, the equivariant \\'etale cohomology algebra $H^*([X/G],\\Lambda)$, where $[X/G]$ is the quotient stack of $X$ by $G$, is finitely generated over $\\Lambda$. Moreover, for coefficients $K \\in D^+_c([X/G],\\mathbb{F}_{\\ell})$ endowed with a commutative multiplicative s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.0365","kind":"arxiv","version":5},"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"}