{"paper":{"title":"An approach to the finitistic dimension conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Fran\\c{c}ois Huard, Marcelo Lanzilotta, Octavio Mendoza","submitted_at":"2007-10-11T19:18:32Z","abstract_excerpt":"Let $R$ be a finite dimensional $k$-algebra over an algebraically closed field $k$ and $\\mathrm{mod} R$ be the category of all finitely generated left $R$-modules. For a given full subcategory $\\mathcal{X}$ of $\\mathrm{mod} R,$ we denote by $\\pfd \\mathcal{X}$ the projective finitistic dimension of $\\mathcal{X}.$ That is, $\\pfd \\mathcal{X}:=\\mathrm{sup} \\{\\pd X : X\\in\\mathcal{X} \\text{and} \\pd X<\\infty\\}.$ \\\n  It was conjectured by H. Bass in the 60's that the projective finitistic dimension $\\pfd (R):=\\pfd (\\mathrm{mod} R)$ has to be finite. Since then, much work has been done toward the proof"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.2328","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"}