{"paper":{"title":"Automatic split-generation for the Fukaya category","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.SG","authors_text":"Nick Sheridan, Timothy Perutz","submitted_at":"2015-10-13T20:01:16Z","abstract_excerpt":"We prove a structural result in mirror symmetry for projective Calabi--Yau (CY) manifolds. Let $X$ be a connected symplectic CY manifold, whose Fukaya category $\\mathcal{F}(X)$ is defined over some suitable Novikov field $\\mathbb{K}$; its mirror is assumed to be some smooth projective scheme $Y$ over $\\mathbb{K}$ with `maximally unipotent monodromy'. Suppose that some split-generating subcategory of (a $\\mathsf{dg}$ enhancement of) $D^bCoh( Y)$ embeds into $\\mathcal{F}(X)$: we call this hypothesis `core homological mirror symmetry'. We prove that the embedding extends to an equivalence of cate"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03848","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"}