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Abelian etale coverings of modular curves over local fields

Teruyoshi Yoshida
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Abstract

We relate a part of the abelian etale fundamental group of curves over local fields to the component group of the Neron model of the jacobian. We apply the result to the modular curve X_0(p)/Q_p to show that the unramified abelian covering X_1(p) over X_0(p) (Shimura covering) uses up all the possible ramification over the special fiber of X_0(p).

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Teruyoshi Yoshida. 2004-05-22. Abelian etale coverings of modular curves over local fields. https://arxiv.org/abs/math/0405426

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