Stable reduction of curves and tame ramification
2010 (English)In: Mathematische Zeitschrift, ISSN 0025-5874, E-ISSN 1432-1823, Vol. 265, no 3, 529-550 p.Article in journal (Refereed) Published
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 l-adic cohomology and vanishing cycles.
Place, publisher, year, edition, pages
2010. Vol. 265, no 3, 529-550 p.
Stable reduction; Tame cyclic quotient singularities; Tame ramification
IdentifiersURN: urn:nbn:se:kth:diva-24226DOI: 10.1007/s00209-009-0528-5ISI: 000277603500003OAI: oai:DiVA.org:kth-24226DiVA: diva2:345640
QC 201008262010-08-262010-08-262010-08-26Bibliographically approved