1101.3647Jan 19, 201150 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

Notes on absolute Hodge classes

François Charles, Christian Schnell

Algebraic Geometry Number Theory

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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.

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