For an etale abelian cover of curves, the Weil Hodge classes on the associated Prym variety are represented by algebraic cycles.
The monodromy of generalized Kummer varieties and algebraic cycles on their intermediate Jacobians.J
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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.