For an etale abelian cover of curves, the Weil Hodge classes on the associated Prym variety are represented by algebraic cycles.
The geometry and fundamental group of permutation products and fat diagonals
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Algebraicity of Hodge classes on some generalized Prym Varieties
For an etale abelian cover of curves, the Weil Hodge classes on the associated Prym variety are represented by algebraic cycles.