Notes on absolute Hodge classes
  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. 
Fran\c{c}ois Charles, Christian Schnell
math.AG math.NT