The Tate Conjectures for Product and Quotient Varieties
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This thesis extends Tate’s conjectures from the smooth case to quotient varieties. It shows that two of those conjectures hold for quotient varieties if they hold for smooth projective varieties. We also consider arbitrary product of modular curves and show that the three conjectures of Tate (in codimension 1) hold for this product. Finally we look at quotients of the surface V = X1(N)×X1(N) and prove that Tate’s conjectures are satisfied for those quotients.