The Tate Conjecture for a family of surfaces of general type with pg = q = 1 and K2 = 3

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 $\Bbb{Q}$, we verify the semisimplicity and Tate conjectures for the Galois representation on the middle $\ell$-adic cohomology of the surface.