{"paper":{"title":"Torelli loci, product cycles, and the homomorphism conjecture for $\\mathcal{A}_g$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Aitor Iribar L\\'opez, Daniel Holmes, Denis Nesterov, Dragos Oprea, Jeremy Feusi, Johannes Schmitt, Lycka Drakengren, Rahul Pandharipande, Samir Canning, Zheming Sun","submitted_at":"2026-01-07T19:38:33Z","abstract_excerpt":"The tautological $\\mathbb{Q}$-subalgebra $\\mathsf{R}^*(\\mathcal{A}_g) \\subset \\mathsf{CH}^*(\\mathcal{A}_g)$ of the Chow ring of the moduli space of principally polarized abelian varieties is generated by the Chern classes of the Hodge bundle. There is a canonical $\\mathbb{Q}$-linear projection operator $\\mathsf{taut}: \\mathsf{CH}^*(\\mathcal{A}_g) \\rightarrow \\mathsf{R}^*(\\mathcal{A}_g).$ We present here new calculations of intersection products of the Torelli locus in $\\mathcal{A}_g$ with the product loci $\\mathcal{A}_{r}\\times \\mathcal{A}_{g-r} \\rightarrow \\mathcal{A}_g$ for $r\\leq 3$. The re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.04353","kind":"arxiv","version":3},"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/2601.04353/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"}