Stable reduction of curves and tame ramification
Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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.
Originalsprog | Engelsk |
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Tidsskrift | Mathematische Zeitschrift |
Vol/bind | 265 |
Udgave nummer | 3 |
Sider (fra-til) | 529-550 |
Antal sider | 22 |
ISSN | 0025-5874 |
DOI | |
Status | Udgivet - 1 jul. 2010 |
ID: 233909977