Soit une courbe lisse définie sur le corps des fractions d’un anneau de valuation discrète . Nous étudions une filtration naturelle sur la fibre spéciale du modèle de Néron de la Jacobienne de 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 sur . 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.
Let be a smooth curve defined over the fraction field of a complete discrete valuation ring . We study a natural filtration of the special fiber of the Néron model of the Jacobian of 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 over , 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 and .
Keywords: Models of curves, tame cyclic quotient singularities, group actions on cohomology, Néron models
Mot clés : modèles des courbes, modèles de Néron, singularitś quotient cycliques modérées, actions de groupe sur la cohomologie
@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}, pages = {853--903}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {60}, number = {3}, year = {2010}, doi = {10.5802/aif.2541}, zbl = {1206.14023}, mrnumber = {2680818}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.2541/} }
TY - JOUR AU - Halle, Lars H. TI - Galois actions on Néron models of Jacobians JO - Annales de l'Institut Fourier PY - 2010 SP - 853 EP - 903 VL - 60 IS - 3 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.2541/ DO - 10.5802/aif.2541 LA - en ID - AIF_2010__60_3_853_0 ER -
Halle, Lars H. Galois actions on Néron models of Jacobians. Annales de l'Institut Fourier, Tome 60 (2010) no. 3, pp. 853-903. doi : 10.5802/aif.2541. http://www.numdam.org/articles/10.5802/aif.2541/
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