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Title of Journal: Math Z

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Abbravation: Mathematische Zeitschrift

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Springer-Verlag

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DOI

10.1016/bs.ctdb.2014.11.008

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1432-1823

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Stable reduction of curves and tame ramification

Authors: Lars Halvard Halle
Publish Date: 2009/04/17
Volume: 265, Issue: 3, Pages: 529-550
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Abstract

We study stable reduction of curves in the case where a tamely ramified base extension is sufficient If X is a smooth curve defined over the fraction field of a strictly henselian discrete valuation ring there is a criterion due to Saito that describes precisely in terms of the geometry of the minimal model with strict normal crossings of X when a tamely ramified extension suffices in order for X to obtain stable reduction For such curves we construct an explicit extension that realizes the stable reduction and we furthermore show that this extension is minimal We also obtain a new proof of Saito’s criterion avoiding the use of ℓadic cohomology and vanishing cycles

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