{"paper":{"title":"Sparseness of t-structures and negative Calabi-Yau dimension in triangulated categories generated by a spherical object","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Dong Yang, Peter Jorgensen, Thorsten Holm","submitted_at":"2011-08-10T15:03:03Z","abstract_excerpt":"Let k be an algebraically closed field and let T be the k-linear algebraic triangulated category generated by a w-spherical object for an integer w. For certain values of w this category is classical. For instance, if w = 0 then it is the compact derived category of the dual numbers over k.\n  As main results of the paper we show that for w \\leq 0, the category T has no non-trivial t-structures, but does have one family of non-trivial co-t-structures, whereas for w \\geq 1 the opposite statement holds.\n  Moreover, without any claim to originality, we observe that for w \\leq -1, the category T is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2195","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"}