{"paper":{"title":"Tautological projection for cycles on the moduli space of abelian varieties","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Dragos Oprea, Rahul Pandharipande, Samir Canning, Sam Molcho","submitted_at":"2024-01-28T21:09:30Z","abstract_excerpt":"We define a tautological projection operator for algebraic cycle classes on the moduli space of principally polarized abelian varieties $\\mathcal{A}_g$: every cycle class decomposes canonically as a sum of a tautological and a non-tautological part. The main new result required for the definition of the projection operator is the vanishing of the top Chern class of the Hodge bundle over the boundary $\\bar{\\mathcal{A}}_g\\smallsetminus \\mathcal{A}_g$ of any toroidal compactification $\\bar{\\mathcal{A}}_g$ of the moduli space $\\mathcal{A}_g$. We prove the vanishing by a careful study of residues i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.15768","kind":"arxiv","version":4},"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/2401.15768/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"}