{"paper":{"title":"Morphisms of 1-motives defined by line bundles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Cristiana Bertolin, Sylvain Brochard","submitted_at":"2016-04-08T15:41:31Z","abstract_excerpt":"Let $S$ be a normal base scheme. The aim of this paper is to study the line bundles on 1-motives defined over $S$. We first compute a d\\'evissage of the Picard group of a 1-motive $M$ according to the weight filtration of $M$. This d\\'evissage allows us to associate, to each line bundle $L$ on $M$, a linear morphism $\\varphi_{L}: M \\rightarrow M^*$ from $M$ to its Cartier dual. This yields a group homomorphism $\\Phi : Pic(M) / Pic(S) \\to Hom(M,M^*)$. We also prove the Theorem of the Cube for 1-motives, which furnishes another construction of the group homomorphism $\\Phi : Pic(M) / Pic(S) \\to H"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.02381","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"}