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Algebraic cycles on hyper-Kähler varieties of generalized Kummer type
Published 9 Aug 2023 in math.AG | (2308.04865v2)
Abstract: We prove the conjectures of Hodge and Tate for any four-dimensional hyper-K\"ahler variety of generalized Kummer type. For an arbitrary variety $X$ of generalized Kummer type, we show that all Hodge classes in the subalgebra of the rational cohomology generated by $H2(X,\mathbb{Q})$ are algebraic.
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