A transfer theorem for Weil classes on Prym--Tyurin factors of Galois covers
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…
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