{"paper":{"title":"Formal loops, Tate objects and tangent Lie algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Benjamin Hennion","submitted_at":"2014-11-29T00:30:17Z","abstract_excerpt":"If $M$ is a symplectic manifold then the space of smooth loops $\\mathrm C^{\\infty}(\\mathrm S^1,M)$ inherits of a quasi-symplectic form. We will focus in this thesis on an algebraic analogue of that result. Kapranov and Vasserot introduced and studied the formal loop space of a scheme $X$. It is an algebraic version of the space of smooth loops in a differentiable manifold.\n  We generalize their construction to higher dimensional loops. To any scheme $X$ -- not necessarily smooth -- we associate $\\mathcal L^d(X)$, the space of loops of dimension $d$. We prove it has a structure of (derived) Tat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.0053","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"}