{"paper":{"title":"On the Algebraic Classification of Module Spectra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.AT","authors_text":"Irakli Patchkoria","submitted_at":"2011-08-31T18:13:29Z","abstract_excerpt":"Using methods developed by Franke, we obtain algebraic classification results for modules over certain symmetric ring spectra ($S$-algebras). In particular, for any symmetric ring spectrum $R$ whose graded homotopy ring $\\pi_*R$ has graded global homological dimension 2 and is concentrated in degrees divisible by some natural number $N \\geq 4$, we prove that the homotopy category of $R$-modules is equivalent to the derived category of the homotopy ring $\\pi_*R$. This improves the Bousfield-Wolbert algebraic classification of isomorphism classes of objects of the homotopy category of $R$-module"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.6309","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"}