Resolution of Nonsingularities of Families of Curves
Akio Tamagawa
Kyoto University, Japan

Abstract
In the present paper, we consider the following problem: For a given closed point x of a special fiber of a generically smooth family X → S of stable curves (with dim(S) = 1), is there a covering Y → X that is generically étale (i.e., étale over the generic fiber(s) of X → S, not only over the generic point(s) of X), where Y is also a family of stable curves, such that the image in X of the non-smooth locus of Y contains x? Among other things, we prove that this is affrmative (possibly after replacing S by a finite extension) in the case where S is the spectrum of a discrete valuation ring of mixed characteristic whose residue field is algebraic over Fp.
Cite this article
Akio Tamagawa, Resolution of Nonsingularities of Families of Curves. Publ. Res. Inst. Math. Sci. 40 (2004), no. 4, pp. 1291–1336
DOI 10.2977/PRIMS/1145475448