Modular Diagonal Quotient Surfaces
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چکیده
Notes: 1) The modular diagonal quotient surfaces as defined above may be viewed as a special case of the general diagonal quotient surfaces studied in Kani/Schanz[7]. 2) The inclusions of subsgroups {1} ≤ ∆αε ≤ G × G induce finite morphisms (both of degree m = |G|) YN Φ → ZN,ε Ψ → Y1 ' P × P. Moreover, by using Shimura’s canonical model X(N)/Q, it can be shown that all these varieties have canonical models over Q (and even over Spec(Z[ 1 N ]). 3) The above curves and surfaces are all projective. For the above-mentioned moduli problem, however, it is also useful to consider the following affine variants. Let
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