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 of a special fiber of a generically smooth family of stable curves (with ), is there a covering that is generically étale (i.e., étale over the generic fiber(s) of , not only over the generic point(s) of ), where is also a family of stable curves, such that the image in of the non-smooth locus of contains ? Among other things, we prove that this is affrmative (possibly after replacing by a finite extension) in the case where is the spectrum of a discrete valuation ring of mixed characteristic whose residue field is algebraic over .

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