{"paper":{"title":"De Rham-Betti Groups of Some Abelian Fourfolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Zekun Ji","submitted_at":"2026-07-25T11:59:53Z","abstract_excerpt":"We determine the de Rham--Betti (dRB) groups for several classes of abelian varieties over $\\bar{\\mathbb{Q}}$. We prove that $\\mathrm{G}_{\\mathrm{dRB}}(A)=\\mathrm{MT}(A)$ for simple CM abelian fourfolds and abelian fourfolds with quartic CM endomorphism field. Due to the current limited knowledge of dRB structures, we adopt an approach different from Moonen--Zarhin's method of determining Mumford-Tate groups. Instead, we use two results by Gross and Chudnovsky, Galois-theoretic analysis and positivity constraints arising from polarizations to exclude certain reductive subgroups of Mumford-Tate"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.23171","kind":"arxiv","version":1},"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/2607.23171/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"}