Algebraic cycles on hyper-Kähler varieties of generalized Kummer type

Abstract

We prove the conjectures of Hodge and Tate for any four-dimensional hyper-Kähler 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 $H^2(X,\mathbb{Q})$ are algebraic.

v2: final version, published on Mathematische Annalen