Stable reduction of curves and tame ramification

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Standard

Stable reduction of curves and tame ramification. / Halle, Lars Halvard.

I: Mathematische Zeitschrift, Bind 265, Nr. 3, 01.07.2010, s. 529-550.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

Halle, LH 2010, 'Stable reduction of curves and tame ramification', Mathematische Zeitschrift, bind 265, nr. 3, s. 529-550. https://doi.org/10.1007/s00209-009-0528-5

APA

Halle, L. H. (2010). Stable reduction of curves and tame ramification. Mathematische Zeitschrift, 265(3), 529-550. https://doi.org/10.1007/s00209-009-0528-5

Vancouver

Halle LH. Stable reduction of curves and tame ramification. Mathematische Zeitschrift. 2010 jul. 1;265(3):529-550. https://doi.org/10.1007/s00209-009-0528-5

Author

Halle, Lars Halvard. / Stable reduction of curves and tame ramification. I: Mathematische Zeitschrift. 2010 ; Bind 265, Nr. 3. s. 529-550.

Bibtex

@article{2e72c7aa4b4c4b38b093d97c1dceb706,
title = "Stable reduction of curves and tame ramification",
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.",
keywords = "Stable reduction, Tame cyclic quotient singularities, Tame ramification",
author = "Halle, {Lars Halvard}",
year = "2010",
month = jul,
day = "1",
doi = "10.1007/s00209-009-0528-5",
language = "English",
volume = "265",
pages = "529--550",
journal = "Mathematische Zeitschrift",
issn = "0025-5874",
publisher = "Springer",
number = "3",

}

RIS

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