{"paper":{"title":"The Ziegler spectrum for derived-discrete algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"David Pauksztello, Kristin Krogh Arnesen, Mike Prest, Rosanna Laking","submitted_at":"2016-03-02T16:16:46Z","abstract_excerpt":"Let $\\Lambda$ be a derived-discrete algebra. We show that the Krull-Gabriel dimension of the homotopy category of projective $\\Lambda$-modules, and therefore the Cantor-Bendixson rank of its Ziegler spectrum, is $2$, thus extending a result of Bobi\\'nski and Krause. We also describe all the indecomposable pure-injective complexes and hence the Ziegler spectrum for derived-discrete algebras, extending a result of Z. Han. Using this, we are able to prove that all indecomposable complexes in the homotopy category of projective $\\Lambda$-modules are pure-injective, so obtaining a class of algebras"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.00775","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"}