Sous-groupes canoniques partiels |
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Authors: | Vincent Pilloni Benoît Stroh |
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Institution: | 1. Columbia University, Rm 535, MC 4441, 2900 Broadway, New York, NY, 10027, USA 2. Université Paris 13, LAGA, 99 Avenue J.B. Clément, 93430, Villetaneuse, France
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Abstract: | 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 ≥ 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 show that there exists a strict neighbourhood of the tube on which this subgroup extends in a finite flat way. On the ordinary stratum and its neighbourhood, we recover the usuel canonical subgroup studied by Abbes and Mokrane, and Andreatta and Gasbarri. |
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