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

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