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arXiv · 1508.01862

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

Christopher Lyons
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Abstract

We prove a big monodromy result for a smooth family of complex algebraic surfaces of general type, with invariants p_g=q=1 and K^2=3, that has been introduced by Catanese and Ciliberto. This is accomplished via a careful study of degenerations. As corollaries, when a surface in this family is defined over a finitely generated extension of Q, we verify the semisimplicity and Tate conjectures for the Galois representation on the middle \ell-adic cohomology of the surface.

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Christopher Lyons. 2015-08-08. The Tate Conjecture for a family of surfaces of general type with p_g=q=1 and K^2=3. https://doi.org/10.1353/ajm.2015.0011

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