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.