On the Tate and Mumford-Tate conjectures in codimension one for varieties with h^{2,0}=1

Abstract

We prove the Tate conjecture for divisor classes and the Mumford-Tate conjecture for the cohomology in degree 2 for varieties with $h^{2,0}=1$ over a finitely generated field of characteristic 0, under a mild assumption on their moduli. As an application of this general result, we prove the Tate and Mumford-Tate conjectures for some classes of algebraic surfaces with $p_g=1$.

Minor corrections, improvements to the exposition. 44 pages, 1 figure

References in corpus (1)

• The Tate Conjecture for a family of surfaces of general type with p_g=q=1 and K^2=3

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• Galois representations on the cohomology of hyper-Kähler varieties
• Arithmetic Deformation of Line Bundles
• A remarkable class of elliptic surfaces of amplitude 1 in weighted projective space