{"paper":{"title":"Generation in singularity categories of hypersurfaces of countable representation type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AC","authors_text":"Kei-ichiro Iima, Maiko Ono, Ryo Takahashi, Tokuji Araya","submitted_at":"2019-01-20T07:47:03Z","abstract_excerpt":"The Orlov spectrum and Rouquier dimension are invariants of a triangulated category to measure how big the category is, and they have been studied actively. In this paper, we investigate the singularity category $\\mathsf{D_{sg}}(R)$ of a hypersurface $R$ of countable representation type. For a thick subcategory $\\mathcal{T}$ of $\\mathsf{D_{sg}}(R)$ and a full subcategory $\\mathcal{X}$ of $\\mathcal{T}$, we calculate the Rouquier dimension of $\\mathcal{T}$ with respect to $\\mathcal{X}$. Furthermore, we prove that the level in $\\mathsf{D_{sg}}(R)$ of the residue field of $R$ with respect to each "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.06636","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"}