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.
Stable reduction of curves and tame ramification / HALLE L,. - In: MATHEMATISCHE ZEITSCHRIFT. - ISSN 0025-5874. - STAMPA. - 265:(2010), pp. 529-550. [10.1007/s00209-009-0528-5]
Stable reduction of curves and tame ramification
HALLE L
2010
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 l-adic cohomology and vanishing cycles.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.