Mathematical Journal of Okayama University volume61 issue1
2019-01 発行

On the existence of non-finite coverings of stable curves over complete discrete valuation rings

Yang, Yu Research Institute for Mathematical Sciences Kyoto University
Publication Date
2019-01
Abstract
Let R be a complete discrete valuation ring with algebraically residue field of characteristic p > 0 and X a stable curve over R. In the present paper, we study the geometry of coverings of X. Under certain assumptions, we prove that, by replacing R by a finite extension of R, there exists a morphism of stable curves f : Y → X over R such that the morphism fη : Yη → Xη induced by f on generic fibers is finite étale and the morphism fs : Ys → Xs induced by f on special fibers is non-finite.
Keywords
stable curve
stable covering
vertical point
admissible covering
Comments
Mathematics Subject Classification. Primary 14H30; Secondary 11G20.