On the prime-to-$p$ part of the groups of connected components of Néron models

Details On the prime-to-$p$ part of the groups of connected components of Néron models On the prime-to-$p$ part of the groups of connected components of Néron models

1994-10-20

arxiv.org/abs/alg-geom/9410020v1

Mathematics

Algebraic Geometry

21 pages, LaTeX, 94-23

Scientific paper

This article improves certain results of Dino Lorenzini concerning the groups of connected components of special fibres of N\'eron models of abelian varieties. Lorenzini has shown the existence of a four step filtration on the prime-to-$p$ part ($p$ is the residue characteristic), and proved certain bounds for the successive quotients. We improve these bounds and show that our bounds are sharp. As an application, we give a complete classification of the groups that can arise as the prime-to-$p$ part of the group of connected components of the Neron model of an abelian variety with given dimensions for the abelian, toric and unipotent part. Hard copies of this preprint are available.

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