{"paper":{"title":"Quaternionic loci in Siegel's modular threefold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Yifan Yang, Yi-Hsuan Lin","submitted_at":"2018-07-02T05:27:23Z","abstract_excerpt":"Let $\\mathcal Q_D$ be the set of moduli points on Siegel's modular threefold whose corresponding principally polarized abelian surfaces have quaternionic multiplication by a maximal order $\\mathcal O$ in an indefinite quaternion algebra of discriminant $D$ over $\\mathbb Q$ such that the Rosati involution coincides with a positive involution of the form $\\alpha\\mapsto\\mu^{-1}\\overline\\alpha\\mu$ on $\\mathcal O$ for some $\\mu\\in\\mathcal O$ with $\\mu^2+D=0$. In this paper, we first give a formula for the number of irreducible components in $\\mathcal Q_D$, strengthening an earlier result of Rotger."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.00466","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":""},"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"}