Abelian Étale Coverings of Modular Curves over Local Fields
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چکیده
We relate a part of the abelian étale fundamental group of curves over local fields to the component group of the Néron model of the jacobian. We apply the result to the modular curve X0(p)/Qp to show that the unramified abelian covering X1(p) → X0(p) (Shimura covering) uses up all the possible ramification over the special fiber of X0(p).
منابع مشابه
Abelian Étale Coverings of Curves over Local Fields and Its Application to Modular Curves
We give a geometric bound of a part of the abelian étale fundamental group of curves over local fields, in particular in the case of bad reduction. We apply the result to the modular curve X0(p)/Qp to show that the unramified abelian covering between X1(p) → X0(p) (Shimura covering) uses up all the possible ramification over the special fiber.
متن کاملAbelian Étale Coverings of Modular Curves over Local Fields
We relate a part of the abelian étale fundamental group of curves over local fields to the component group of the Néron model of the jacobian. We apply the result to the modular curve X0(p)/Qp to show that the unramified abelian covering X1(p) → X0(p) (Shimura covering) uses up all the possible ramification over the special fiber of X0(p).
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تاریخ انتشار 2004