#### DOCUMENTA MATHEMATICA, Vol. 21 (2016), 1691-1713

Johan Commelin

The Mumford--Tate Conjecture for the Product of an Abelian Surface and a K3 Surface

The Mumford--Tate conjecture is a precise way of saying that the Hodge structure on singular cohomology conveys the same information as the Galois representation on $\ell$-adic étale cohomology, for an algebraic variety over a finitely generated field of characteristic 0. This paper presents a proof of the Mumford--Tate conjecture in degree 2 for the product of an abelian surface and a K3 surface.

2010 Mathematics Subject Classification: Primary 14C15; Secondary 14C30, 11G10, 14J28.

Keywords and Phrases: Mumford--Tate conjecture, abelian surface, K3 surface.

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