{"paper":{"title":"The Mumford--Tate conjecture for products of abelian varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Johan Commelin","submitted_at":"2018-04-18T17:59:11Z","abstract_excerpt":"Let $X$ be a smooth projective variety over a finitely generated field $K$ of characteristic~$0$ and fix an embedding $K \\subset \\mathbb{C}$. The Mumford--Tate conjecture is a precise way of saying that certain extra structure on the $\\ell$-adic \\'etale cohomology groups of~$X$ (namely, a Galois representation) and certain extra structure on the singular cohomology groups of~$X$ (namely, a Hodge structure) convey the same information.\n  The main result of this paper says that if $A_1$ and~$A_2$ are abelian varieties (or abelian motives) over~$K$, and the Mumford--Tate conjecture holds for both"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.06840","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"}