{"paper":{"title":"Purity and 2-Calabi-Yau categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Ben Davison","submitted_at":"2021-06-14T18:16:29Z","abstract_excerpt":"For various 2-Calabi-Yau categories $\\mathscr{C}$ for which the stack of objects $\\mathfrak{M}$ has a good moduli space $p\\colon\\mathfrak{M}\\rightarrow \\mathcal{M}$, we establish purity of the mixed Hodge module complex $p_{!}\\underline{\\mathbb{Q}}_{\\mathfrak{M}}$. We do this by using formality in 2CY categories, along with \\'etale neighbourhood theorems for stacks, to prove that the morphism $p$ is modelled \\'etale-locally by the semisimplification morphism from the stack of modules of a preprojective algebra. Then via the integrality theorem in cohomological Donaldson-Thomas theory we prove "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.07692","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2106.07692/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}