{"paper":{"title":"Schematic homotopy types and non-abelian Hodge theory","license":"","headline":"","cross_cats":["math.AT"],"primary_cat":"math.AG","authors_text":"B. Toen, L. Katzarkov, T. Pantev","submitted_at":"2001-07-18T14:25:50Z","abstract_excerpt":"In this work we use Hodge theoretic methods to study homotopy types of complex projective manifolds with arbitrary fundamental groups. The main tool we use is the \\textit{schematization functor} $X \\mapsto (X\\otimes \\mathbb{C})^{sch}$, introduced by the third author as a substitute for the rationalization functor in homotopy theory in the case of non-simply connected spaces. Our main result is the construction of a \\textit{Hodge decomposition} on $(X\\otimes\\mathbb{C})^{sch}$. This Hodge decomposition is encoded in an action of the discrete group $\\mathbb{C}^{\\times \\delta}$ on the object $(X\\o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0107129","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"}