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Galois actions on Néron models of Jacobians

Lars H. Halle (2010)

Annales de l’institut Fourier

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...

Galois Covers and the Hilbert-Grunwald Property

Pierre Dèbes, Nour Ghazi (2012)

Annales de l’institut Fourier

Our main result combines three topics: it contains a Grunwald-Wang type conclusion, a version of Hilbert’s irreducibility theorem and a p -adic form à la Harbater, but with good reduction, of the Regular Inverse Galois Problem. As a consequence we obtain a statement that questions the RIGP over . The general strategy is to study and exploit the good reduction of certain twisted models of the covers and of the associated moduli spaces.

General theory of Lie derivatives for Lorentz tensors

Lorenzo Fatibene, Mauro Francaviglia (2011)

Communications in Mathematics

We show how the ad hoc prescriptions appearing in 2001 for the Lie derivative of Lorentz tensors are a direct consequence of the Kosmann lift defined earlier, in a much more general setting encompassing older results of Y. Kosmann about Lie derivatives of spinors.

Groupe de Picard des variétés de modules de faisceaux semi-stables sur 2 ( )

Jean-Marc Drezet (1988)

Annales de l'institut Fourier

Le sujet de cet article est le groupe de Picard de la variété de modules M ( r , c 1 , c 2 ) des faisceaux algébriques semi-stables de rang r et de classes de Chern c 1 , c 2 sur P 2 ( C ) . Le premier résultat est que M ( r , c 1 , c 2 ) est localement factorielle, ce qui permet d’identifier Pic ( M ( r , c 1 , c 2 ) ) et le groupe des classes d’équivalence linéaire des diviseurs de Weil de M ( r , c 1 , c 2 ) ) . Il existe une unique application δ : Q Q telle que dim ( M ( r , c 1 , c 2 ) ) > 0 si et seulement si ( c 2 - ( r - 1 ) c 1 2 / 2 r ) / r > δ ( c 1 / r ) . Si on a égalité, Pic ( M ( r , c 1 , c 2 ) ) est isomorphe à Z , et si l’inégalité est stricte, Pic ( M ( r , c 1 , c 2 ) ) est isomorphe à Z 2 . On donne ensuite...

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