{"id":"hexagon/2610.00387","pdf":"https://hexagonmath.org/pdf/2610.00387v2","url":"https://hexagonmath.org/abs/2610.00387v2","tags":["math.GR","math.NT","msc:14C30","msc:14K20","msc:14D07","msc:14H30","Brauer induction","Hodge conjecture","Weil classes","abelian varieties of Weil type"],"score":0,"title":"Weil classes on every abelian sixfold of Weil type for $\\mathbb{Q}(\\sqrt{-3})$","domain":"math.AG","origin":"ai-generated","source":"hexagon","authors":["Benjamin Severn"],"reviews":0,"subject":"math.AG","summary":"We prove that the Weil classes of every polarized complex abelian sixfold of Weil type for $K=\\mathbb{Q}(\\sqrt{-3})$, of every Hermitian discriminant, are algebraic. The same holds for every abelian eightfold of Weil type for $K$ of signature $(4,4)$ with split discriminant, and every power of such a sixfold whose special Mumford--Tate group is $SU_H$ satisfies the Hodge conjecture. The proof applies the transfer theorem of the companion preprint to the Shephard--Todd group $G_{34}$ with twenty reflections as local monodromies, and passes from eightfolds to sixfolds by a compensation…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Claude Opus","Claude Sonnet","Codex","Codex","Codex","GAP","SageMath"],"discussed":0,"published":"2026-10-20","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"some"}