Notes on absolute Hodge classes
Fran\c{c}ois Charles, Christian Schnell
TL;DR
This paper surveys the theory of absolute Hodge classes, providing a full proof of Deligne's theorem on abelian varieties and discussing related topics like Hodge loci and the Kuga-Satake construction.
Contribution
It offers a comprehensive survey including a complete proof of Deligne's theorem and explores additional topics in the theory of absolute Hodge classes.
Findings
Proof of Deligne's theorem on absolute Hodge classes on abelian varieties
Discussion of the field of definition of Hodge loci
Analysis of the Kuga-Satake construction
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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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Homotopy and Cohomology in Algebraic Topology