Galois actions on Néron models of Jacobians

Lars H. Halle[1]

  • [1] Gottfried Wilhelm Leibniz Universität Hannover Institut für Algebraische Geometrie Welfengarten 1 30167 Hannover (Deutschland)

Annales de l’institut Fourier (2010)

  • Volume: 60, Issue: 3, page 853-903
  • ISSN: 0373-0956

Abstract

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Let X be a smooth curve defined over the fraction field K of a complete discrete valuation ring R . We study a natural filtration of the special fiber of the Néron model of the Jacobian of X by closed, unipotent subgroup schemes. We show that the jumps in this filtration only depend on the fiber type of the special fiber of the minimal regular model with strict normal crossings for X over R , and in particular are independent of the residue characteristic. Furthermore, we obtain information about where these jumps occur. We also compute the jumps for each of the finitely many possible fiber types for curves of genus 1 and 2 .

How to cite

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Halle, Lars H.. "Galois actions on Néron models of Jacobians." Annales de l’institut Fourier 60.3 (2010): 853-903. <http://eudml.org/doc/116294>.

@article{Halle2010,
abstract = {Let $X$ be a smooth curve defined over the fraction field $K$ of a complete discrete valuation ring $R$. We study a natural filtration of the special fiber of the Néron model of the Jacobian of $X$ by closed, unipotent subgroup schemes. We show that the jumps in this filtration only depend on the fiber type of the special fiber of the minimal regular model with strict normal crossings for $X$ over $R$, and in particular are independent of the residue characteristic. Furthermore, we obtain information about where these jumps occur. We also compute the jumps for each of the finitely many possible fiber types for curves of genus $1$ and $2$.},
affiliation = {Gottfried Wilhelm Leibniz Universität Hannover Institut für Algebraische Geometrie Welfengarten 1 30167 Hannover (Deutschland)},
author = {Halle, Lars H.},
journal = {Annales de l’institut Fourier},
keywords = {Models of curves; tame cyclic quotient singularities; group actions on cohomology; Néron models; tame cyclic quotient singularities,},
language = {eng},
number = {3},
pages = {853-903},
publisher = {Association des Annales de l’institut Fourier},
title = {Galois actions on Néron models of Jacobians},
url = {http://eudml.org/doc/116294},
volume = {60},
year = {2010},
}

TY - JOUR
AU - Halle, Lars H.
TI - Galois actions on Néron models of Jacobians
JO - Annales de l’institut Fourier
PY - 2010
PB - Association des Annales de l’institut Fourier
VL - 60
IS - 3
SP - 853
EP - 903
AB - Let $X$ be a smooth curve defined over the fraction field $K$ of a complete discrete valuation ring $R$. We study a natural filtration of the special fiber of the Néron model of the Jacobian of $X$ by closed, unipotent subgroup schemes. We show that the jumps in this filtration only depend on the fiber type of the special fiber of the minimal regular model with strict normal crossings for $X$ over $R$, and in particular are independent of the residue characteristic. Furthermore, we obtain information about where these jumps occur. We also compute the jumps for each of the finitely many possible fiber types for curves of genus $1$ and $2$.
LA - eng
KW - Models of curves; tame cyclic quotient singularities; group actions on cohomology; Néron models; tame cyclic quotient singularities,
UR - http://eudml.org/doc/116294
ER -

References

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