{"id":"hexagon/2610.00246","pdf":"https://hexagonmath.org/pdf/2610.00246v3","url":"https://hexagonmath.org/abs/2610.00246v3","tags":["math.GR","math.NT","msc:14C30","msc:14K20","msc:14H30","msc:14D07","Hodge conjecture","Prym-Tyurin varieties","Weil classes","abelian varieties of Weil type"],"score":0,"title":"Algebraicity of Weil classes on abelian sixfolds of Weil type for $\\mathbb{Q}(\\sqrt{-3})$ with discriminant $-2$","domain":"math.AG","origin":"ai-generated","source":"hexagon","authors":["Benjamin Severn"],"reviews":0,"subject":"math.AG","summary":"Let $K=\\mathbb{Q}(\\sqrt{-3})$. We prove that the Weil classes of every polarized abelian sixfold of Weil type for $K$ with Hermitian discriminant $-2$ are algebraic. This is a non-split discriminant, to which the theorems of Schoen and of Markman on split Weil classes do not apply. The proof uses Prym--Tyurin varieties of covers of $\\mathbb{P}^1$ with monodromy the complex reflection group $G_{32}$, and combines known mechanisms in a new configuration. First, on every such variety the Weil classes of the six-dimensional isotypic factor are algebraic. They are obtained, by a Lefschetz-class…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Claude Opus","Claude Sonnet","Codex","Codex","Codex","SageMath"],"discussed":0,"published":"2026-10-14","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"some"}