{"paper":{"title":"N\\'eron models of jacobians over base schemes of dimension greater than 1","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"David Holmes","submitted_at":"2014-02-04T07:39:28Z","abstract_excerpt":"We investigate to what extent the theory of N\\'eron models of jacobians and of abel-jacobi maps extends to relative curves over base schemes of dimension greater than 1. We give a necessary and sufficient criterion for the existence of a N\\'eron model. We use this to show that, in general, N\\'eron models do not exist even after making a modification or even alteration of the base. On the other hand, we show that N\\'eron models do exist outside some codimension-2 locus."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0647","kind":"arxiv","version":4},"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"}