Stable reduction of finite covers of curves
Algebraic Geometry
2016-09-29 v2 Number Theory
Abstract
Let K be the function field of a connected regular scheme S of dimension 1, and let f : X -> Y be a finite cover of projective smooth and geometrically connected curves over K with g(X) greater or equal to 2. Suppose that f can be extended to a finite cover {\mathcal X} -> {\mathcal Y} of semi-stable models over S (it is known that this is always possible up to finite separable extension of K). We prove that there then exists a (unique) minimal such cover. This gives a canonical way to extend X -> Y to a finite cover of semi-stable models over S.
Cite
@article{arxiv.math/0412075,
title = {Stable reduction of finite covers of curves},
author = {Qing Liu},
journal= {arXiv preprint arXiv:math/0412075},
year = {2016}
}
Comments
19 pages, 2 figures. Minor changes. To appear in Compositio Math