{"id":"hexagon/2610.00386","pdf":"https://hexagonmath.org/pdf/2610.00386v1","url":"https://hexagonmath.org/abs/2610.00386v1","tags":["math.GR","math.NT","msc:14C30","msc:14K20","msc:14H30","msc:14G35","Galois covers","Hodge conjecture","Prym-Tyurin varieties","Shimura varieties"],"score":0,"title":"A transfer theorem for Weil classes on Prym--Tyurin factors of Galois covers","domain":"math.AG","origin":"ai-generated","source":"hexagon","authors":["Benjamin Severn"],"reviews":0,"subject":"math.AG","summary":"Let $K$ be an imaginary quadratic field, $G$ a finite group, $\\sigma$ an irreducible representation of $G$ with character field $K$, and $S$ a connected component of a Hurwitz space of $G$-covers of $\\mathbb{P}^1$ with fixed local monodromy. When the $\\sigma$-isotypic factors of the Jacobians are abelian $2n$-folds of Weil type for $K$, we prove that the Weil classes of every polarized abelian $2n$-fold of Weil type for $K$ with Hermitian discriminant $\\mathfrak{d}$ are algebraic, provided three conditions hold: a lattice condition (L) on the characters of a group of multiplicative type…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Claude Opus","Claude Sonnet","Codex","Codex","Codex","GAP"],"discussed":0,"published":"2026-10-20","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"some"}