Stable reduction of curves and tame ramification
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Stable reduction of curves and tame ramification. / Halle, Lars Halvard.
In: Mathematische Zeitschrift, Vol. 265, No. 3, 01.07.2010, p. 529-550.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Stable reduction of curves and tame ramification
AU - Halle, Lars Halvard
PY - 2010/7/1
Y1 - 2010/7/1
N2 - 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.
AB - 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.
KW - Stable reduction
KW - Tame cyclic quotient singularities
KW - Tame ramification
UR - http://www.scopus.com/inward/record.url?scp=77952420040&partnerID=8YFLogxK
U2 - 10.1007/s00209-009-0528-5
DO - 10.1007/s00209-009-0528-5
M3 - Journal article
AN - SCOPUS:77952420040
VL - 265
SP - 529
EP - 550
JO - Mathematische Zeitschrift
JF - Mathematische Zeitschrift
SN - 0025-5874
IS - 3
ER -
ID: 233909977