Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



A logarithmic view towards semistable reduction

Author: Jakob Stix
Journal: J. Algebraic Geom. 14 (2005), 119-136
Published electronically: June 24, 2004
MathSciNet review: 2092128
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Abstract: A smooth, proper family of curves creates a monodromy action of the fundamental group of the base on the ${\rm H}^1$ of a fibre. The geometric condition of T. Saito for the action of the wild inertia of a boundary point to be trivial is transformed to the condition of logarithmic smooth reduction. The proof emphasizes methods and results from logarithmic geometry. It applies to quasi-projective smooth curves with étale boundary divisor.

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Jakob Stix
Affiliation: Mathematisches Institut, Universität Bonn, Beringstraße 1, 53115 Bonn, Germany

Received by editor(s): May 13, 2003
Received by editor(s) in revised form: February 10, 2004
Published electronically: June 24, 2004
Additional Notes: The author acknowledges the financial support provided through the European Community’s Human Potential Program under contract HPRN-CT-2000-00114, GTEM