{"paper":{"title":"A rigid analytic proof that the Abel-Jacobi map extends to compact-type models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Joseph Rabinoff, Taylor Dupuy","submitted_at":"2017-05-08T18:23:39Z","abstract_excerpt":"Let $K$ be a non-Archimedean valued field with valuation ring $R$. Let $C_\\eta$ be a $K$-curve with compact type reduction, so its Jacobian $J_\\eta$ extends to an abelian $R$-scheme $J$. We prove that an Abel-Jacobi map $\\iota\\colon C_\\eta\\to J_\\eta$ extends to a morphism $C\\to J$, where $C$ is a compact-type $R$-model of $J$, and we show this is a closed immersion when the special fiber of $C$ has no rational components. To do so, we apply a rigid-analytic \"fiberwise\" criterion for a finite morphism to extend to integral models, and geometric results of Bosch and L\\\"utkebohmert on the analyti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.03034","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"}