Algebraic cycles on hyper-Kähler varieties of generalized Kummer type

We prove the conjectures of Hodge and Tate for any four-dimensional hyper-K & auml;hler 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,Q)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H<^>2(X,\mathbb {Q})$$\end{document} are algebraic.