{"paper":{"title":"Gorenstein categories, singular equivalences and finite generation of cohomology rings in recollements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.KT"],"primary_cat":"math.RT","authors_text":"Chrysostomos Psaroudakis, {\\O}ystein Skarts{\\ae}terhagen, {\\O}yvind Solberg","submitted_at":"2014-02-07T10:15:12Z","abstract_excerpt":"Given an artin algebra $\\Lambda$ with an idempotent element $a$ we compare the algebras $\\Lambda$ and $a\\Lambda a$ with respect to Gorensteinness, singularity categories and the finite generation condition Fg for the Hochschild cohomology. In particular, we identify assumptions on the idempotent element $a$ which ensure that $\\Lambda$ is Gorenstein if and only if $a\\Lambda a$ is Gorenstein, that the singularity categories of $\\Lambda$ and $a\\Lambda a$ are equivalent and that Fg holds for $\\Lambda$ if and only if Fg holds for $a\\Lambda a$. We approach the problem by using recollements of abelia"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.1588","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"}