Abelian etale coverings of modular curves over local fields

Details Abelian etale coverings of modular curves over local fields Abelian etale coverings of modular curves over local fields

2004-05-22

arxiv.org/abs/math/0405426v1

Mathematics

Number Theory

13 pages

Scientific paper

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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