{"paper":{"title":"Calculating with topological Andr\\'e-Quillen theory, I: Homotopical properties of universal derivations and free commutative $S$-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Andrew Baker","submitted_at":"2012-08-09T10:40:54Z","abstract_excerpt":"We adopt the viewpoint that topological And\\'e-Quillen theory for commutative $S$-algebras should provide usable (co)homology theories for doing calculations in the sense traditional within Algebraic Topology. Our main emphasis is on homotopical properties of universal derivations, especially their behaviour in multiplicative homology theories. There are algebraic derivation properties, but also deeper properties arising from the homotopical structure of the free algebra functor $\\mathbb{P}_R$ and its relationship with extended powers of spectra. In the connective case in ordinary $\\bmod{\\,p}$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.1868","kind":"arxiv","version":8},"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"}