arXiv 0907.16822009-07math.AGmath.NT

Partial canonical subgroups

Vincent Pilloni, Benoit Stroh

英文摘要：

The reduction of Siegel varieties modulo a prime number p is stratified by the multiplicative rank of the p-divisible group of the universal abelian variety. For r\geq 0 the maximal multiplicative subgroup of the restriction of the p-torsion group of the universal abelian variety to the r-th stratum lifts canonically to the tube of this stratum and defines a partial canonical subgroup of rank r. We prove that this subgroup extends in a finite flat way on some strict neighborhood of the tube. On the ordinary stratum and on its neighborhood, we recover the usual canonical subgroup considered by Abbes and Mokrane, and Andreatta and Gasbarri. ----- La reduction des varietes de Siegel modulo un nombre premier p est stratifiee par le rang multiplicatif du groupe p-divisible de la variete abelienne universelle. Pour r\geq 0, le sous-groupe multiplicatif maximal de la restriction du groupe de p-torsion de la variete abelienne universelle a la r-ieme strate se releve canoniquement sur le tube de cette strate et definit un sous-groupe canonique partiel de rang r. Nous montrons qu'il existe un voisinage strict du tube sur lequel ce sous-groupe s'etend de maniere finie et plate. Sur la strate ordinaire et au voisinage de celle-ci, on retrouve le sous-groupe canonique usuel etudie par Abbes et Mokrane d'une part, Andreatta et Gasbarri d'autre part.

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