THE TATE CONJECTURE FOR A FAMILY OF SURFACES OF GENERAL TYPE WITH pg
نویسنده
چکیده
We prove a big monodromy result for a smooth family of complex algebraic surfaces of general type, with invariants pg = 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 `-adic cohomology of the surface.
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