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

1994/10/20 by Bas Edixhoven, Edixhoven, Bas
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #alg-geom #math.AG

paper · pdf · doi:10.48550/arxiv.alg-geom/9410020

21 pages, LaTeX, 94-23

arxiv created 1994/10/20 · openalex publication_date 1994/10/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This article improves certain results of Dino Lorenzini concerning the groups of connected components of special fibres of Néron 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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