Real multiplication on K3 surfaces and Kuga Satake varieties

Details Real multiplication on K3 surfaces and Kuga Satake varieties Real multiplication on K3 surfaces and Kuga Satake varieties

2006-09-29

arxiv.org/abs/math/0609839v1

Mathematics

Algebraic Geometry

Scientific paper

The endomorphism algebra of a K3 type Hodge structure is a totally real field or a CM field. In this paper we give a low brow introduction to the case of a totally real field. We give existence results for the Hodge structures, for their polarizations and for certain K3 surfaces. We consider the Kuga Satake variety of these Hodge structures and we discuss some examples. Finally we indicate various open problems related to the Hodge conjecture.

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