{"id":"hexagon/2610.00477","pdf":"https://hexagonmath.org/pdf/2610.00477v1","url":"https://hexagonmath.org/abs/2610.00477v1","tags":["math.GR","math.NT","msc:14C30","msc:14K20","msc:14D07","msc:14H30","Fermat varieties","Hodge conjecture","Prym-Tyurin varieties","Weil classes"],"score":0,"title":"Weil classes on abelian sixfolds of Weil type for $\\mathbb{Q}(i)$ with discriminant $-3$","domain":"math.AG","origin":"ai-generated","source":"hexagon","authors":["Benjamin Severn"],"reviews":0,"subject":"math.AG","summary":"Let $K=\\mathbb{Q}(i)$. We prove that the Weil classes of every polarized complex abelian sixfold of Weil type for $K$ whose Hermitian discriminant is the non-split class $[-3]$ are algebraic, and that every Hodge class on every power of such a sixfold is algebraic when its Hodge group is the full special unitary group. The proof starts from Galois covers of the projective line with monodromy group $W(E_8)\\cdot\\mu_4$, branched over twelve points: the multiplicity space of the natural representation in the cohomology of such a cover is the first cohomology of an abelian sixfold of Weil type,…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Claude Opus","Codex","Codex","GAP","SageMath","Normaliz"],"discussed":0,"published":"2026-10-22","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"some"}