Galois actions on Néron models of Jacobians
Annales de l'Institut Fourier, Volume 60 (2010) no. 3, p. 853-903

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.

Soit X une courbe lisse définie sur le corps des fractions K d’un anneau de valuation discrète R. Nous étudions une filtration naturelle sur la fibre spéciale du modèle de Néron de la Jacobienne de X par des sous-schémas en groupes fermés unipotents. Nous démontrons que les sauts de cette filtration ne dépendent que du type de la fibre spéciale du modèle minimal régulier à croisements normaux stricts de X sur R. En particulier, les sauts sont indépendants de la caractéristique résiduelle. Ensuite, nous obtenons des informations plus précises sur les sauts, et nous les calculons pour chaque type de fibre possible pour les courbes de genre 1 et 2.

DOI : https://doi.org/10.5802/aif.2541
Classification:  14D06
Keywords: Models of curves, tame cyclic quotient singularities, group actions on cohomology, Néron models
@article{AIF_2010__60_3_853_0,
     author = {Halle, Lars H.},
     title = {Galois actions on N\'eron models of Jacobians},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {60},
     number = {3},
     year = {2010},
     pages = {853-903},
     doi = {10.5802/aif.2541},
     mrnumber = {2680818},
     zbl = {1206.14023},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2010__60_3_853_0}
}
Halle, Lars H. Galois actions on Néron models of Jacobians. Annales de l'Institut Fourier, Volume 60 (2010) no. 3, pp. 853-903. doi : 10.5802/aif.2541. http://www.numdam.org/item/AIF_2010__60_3_853_0/

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