2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78266This paper gives an introduction to Kuga-Satake varieties and discusses some aspects of the Hodge conjecture related to them. Kuga-Satake varieties are abelian varieties associated to certain weight two Hodge structures, for example the second cohomology group of a K3 surface. We give a detailed account of the construction of Kuga-Satake varieties and of their decomposition in simple subvarieties. We recall the Hodge conjecture and we point out a connection between the Hodge conjecture for abelian fourfolds and Kuga-Satake varieties. We discuss the implications of the Hodge conjecture on the geometry of surfaces whose second cohomology group has a Kuga-Satake variety. We conclude with some recent results on Kuga-Satake varieties of Hodge structures on which an imaginary quadratic field acts.23 pages LaTeX. To appear in: The Arithmetic and Geometry of Algebraic Cycles. Eds. J. Lewis et al. (Proceedings of the NATO ASI and CRM Summer School in Banff, 1998)Algebraic Geometrytext