Abelian etale coverings of modular curves over local fields
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 X0(p)/Qp to show that the unramified abelian covering X1(p) over X0(p) (Shimura covering) uses up all the possible ramification over the special fiber of X0(p).
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