Log smooth extension of a family of curves and semistable reduction
Author:
Takeshi Saito
Journal:
J. Algebraic Geom. 13 (2004), 287321
DOI:
https://doi.org/10.1090/S1056391103003382
Published electronically:
December 3, 2003
MathSciNet review:
2047700
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Abstract  References  Additional Information
Abstract: We show that a family of smooth stable curves defined on the interior of a log regular scheme is extended to a log smooth scheme over the whole log regular scheme, if it is so at each generic point of the boundary, under a very mild assumption. We also include a proof of the fact that a log smooth scheme over a discrete valuation ring has potentially a semistable model. As a consequence, we show that a hyperbolic polycurve in the sense of Mochizuk over a discrete valuation field has potentially a proper semistable model if the characteristic of the residue field is sufficiently large.

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Additional Information
Takeshi Saito
Affiliation:
Department of Mathematics, University of Tokyo, Tokyo 1538914 Japan
MR Author ID:
236565
Email:
tsaito@ms.utokyo.ac.jp
Received by editor(s):
October 3, 2001
Published electronically:
December 3, 2003