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 Q, we verify the semisimplicity and Tate conjectures for the Galois representation on the middle l-adic cohomology of the surface.