Rational points of the group of components of a Neron model

Abstract

Let A_K be an abelian variety over a discrete valuation field K. Let A be the Neron model of A_K over the ring of integers O_K of K and A_k its special fibre. We study the set of rational points of the group of components ϕ_A of A_k. In particular, we look at the cases where A_K is a Jacobian or where A_K is an abelian variety having semi-stable reduction. We also consider algebraic tori over K instead of abelian varieties.

16 pages

Cited by in corpus (10)

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• The index of an algebraic variety
• Arithmetic of hyperelliptic curves over local fields
• Self-duality of Selmer groups
• Canonical Heights on Genus Two Jacobians
• Corrigendum to Néron models, Lie algebras, and reduction of curves of genus one [LLR1] and The Brauer group of a surface [LLR2]
• Special Values of the Zeta Function of an Arithmetic Surface
• Groups of components of Néron models of Jacobians and Brauer groups
• Values of zeta functions of arithmetic surfaces at $s=1$
• Local constancy of reduction type and related invariants for curves in $p$-adic families