Compactifications de variétés de Siegel aux places de mauvaise réduction

Abstract : In this thesis, we construct compactifications of Siegel modular varieties at bad reduction places of parahoric type. We first construct the toroidal compactifications, which are quite explicit and whose singularities are controlled. These compactifications are not canonical, but depend on some combinatorial choice. The main point in our construction is an approximation of Mumford degenerating abelian varieties that preserves a torsion subgroup. This allows us to glue together the different local charts of the compactifications. We use these results to construct the minimal compactifications, which are canonical but less explicit and more singular. As an application, we give a new proof of the existence of the canonical subgroup for abelian varieties.
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https://hal.univ-lorraine.fr/tel-01748496
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Benoît Stroh. Compactifications de variétés de Siegel aux places de mauvaise réduction. Mathématiques générales [math.GM]. Université Henri Poincaré - Nancy 1, 2008. Français. ⟨NNT : 2008NAN10109⟩. ⟨tel-01748496⟩

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