Notes on absolute Hodge classes

Abstract

We survey the theory of absolute Hodge classes. The notes include a full proof of Deligne's theorem on absolute Hodge classes on abelian varieties as well as a discussion of other topics, such as the field of definition of Hodge loci and the Kuga-Satake construction.

50 pages. This text is an expanded version of lectures given at the ICTP summer school on Hodge theory and related topics in Trieste in June 2010