{"paper":{"title":"$n$-excisive functors, canonical connections, and line bundles on the Ran space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"James Tao","submitted_at":"2019-06-19T08:52:58Z","abstract_excerpt":"Let $X$ be a smooth algebraic variety over $k$. We prove that any flat quasicoherent sheaf on $\\operatorname{Ran}(X)$ canonically acquires a D-module structure. In addition, we prove that, if the geometric fiber $X_{\\overline{k}}$ is connected and admits a smooth compactification, then any line bundle on $S \\times \\operatorname{Ran}(X)$ is pulled back from $S$, for any locally Noetherian $k$-scheme $S$. Both theorems rely on a family of results which state that the (partial) limit of an $n$-excisive functor defined on the category of pointed finite sets is trivial."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.07976","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"}