Stable reduction of curves and tame ramification
Research output: Contribution to journal › Journal article › Research › peer-review
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.
Original language | English |
---|---|
Journal | Mathematische Zeitschrift |
Volume | 265 |
Issue number | 3 |
Pages (from-to) | 529-550 |
Number of pages | 22 |
ISSN | 0025-5874 |
DOIs | |
Publication status | Published - 1 Jul 2010 |
- Stable reduction, Tame cyclic quotient singularities, Tame ramification
Research areas
ID: 233909977