{"paper":{"title":"On the Abelian Fundamental Group Scheme of a Family of Varities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Marco Antei","submitted_at":"2009-12-29T15:25:53Z","abstract_excerpt":"Let $S$ be a connected Dedekind scheme and $X$ an $S$-scheme provided with a section $x$. We prove that the morphism of fundamental group schemes $\\pi_1(X,x)^{ab}\\to \\pi_1(\\mathbf{Alb}_{X/S},0_{\\mathbf{Alb}_{X/S}})$ induced by the canonical morphism from $X$ to its Albanese scheme $\\mathbf{Alb}_{X/S}$ (when the latter exists) fits in an exact sequence of group schemes $0\\to (\\mathbf{NS}^{\\tau}_{X/S})^{\\vee}\\to \\pi_1(X,x)^{ab}\\to \\pi_1(\\mathbf{Alb}_{X/S},0_{\\mathbf{Alb}_{X/S}}) \\to 0$ where the kernel is a finite and flat $S$-group scheme. Furthermore we prove that any finite and commutative qu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0912.5319","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":""},"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"}