{"paper":{"title":"Abelian varieties genuinely of $\\mathrm{GL}_n$-type","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Enric Florit, Francesc Fit\\'e, Xavier Guitart","submitted_at":"2024-12-30T18:53:23Z","abstract_excerpt":"A simple abelian variety $A$ defined over a number field $k$ is called of $\\mathrm{GL}_n$-type if there exists a number field of degree $2\\dim(A)/n$ which is a subalgebra of $\\mathrm{End}^0(A)$. We say that $A$ is genuinely of $\\mathrm{GL}_n$-type if its base change $A_{\\overline{k}}$ contains no isogeny factor of $\\mathrm{GL}_m$-type for $m<n$. This generalizes the classical notion of abelian variety of $\\mathrm{GL}_2$-type without potential complex multiplication introduced by Ribet. We develop a theory of building blocks, inner twists and nebentypes for these varieties. When the center of $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.21183","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.21183/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"}