{"paper":{"title":"The N\\'eron model of a higher-dimensional Lagrangian fibration","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Yoon-Joo Kim","submitted_at":"2024-10-28T16:36:36Z","abstract_excerpt":"Let $\\pi : X \\to B$ be a projective Lagrangian fibration of a smooth symplectic variety $X$ to a smooth variety $B$. Denote the complement of the discriminant locus by $B_0 = B \\setminus \\operatorname{Disc}(\\pi)$, its preimage by $X_0 = \\pi^{-1}(B_0)$, and the complement of the critical locus by $X' = X \\setminus \\operatorname{Sing}(\\pi)$. Under an assumption that the morphism $X' \\to B$ is surjective, we construct (1) the N\\'eron model of the abelian fibration $\\pi_0 : X_0 \\to B_0$ and (2) the N\\'eron model of its automorphism abelian scheme $\\operatorname{Aut}^{\\circ}_{\\pi_0} \\to B_0$. Contr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.21193","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/2410.21193/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"}