{"paper":{"title":"Hodge Groups of Hodge Structures with Hodge Numbers $(n,0,\\ldots,0,n)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Laure Flapan","submitted_at":"2015-11-11T03:55:42Z","abstract_excerpt":"This paper studies the possible Hodge groups of simple polarizable $\\mathbb{Q}$-Hodge structures with Hodge numbers $(n,0,\\ldots,0,n)$. In particular, it generalizes earlier work of Ribet and Moonen-Zarhin to completely determine the possible Hodge groups of such Hodge structures when $n$ is equal to $1$, $4$, or a prime $p$. In addition, the paper determines possible Hodge groups, under certain conditions on the endomorphism algebra, when $n=2p$, for $p$ an odd prime. A consequence of these results is that both the Hodge and General Hodge Conjectures hold for all powers of a simple $2p$-dimen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.03379","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"}