Department of Mathematics and Computer Science Bar-Ilan University Institut de Mathématiques de Jussieu, CNRS UMR 9994 Université de Paris-VII-Denis-Diderot UFR de Mathématiques
We study a problem of constructing an algebraic torus (an abelian variety) over a p-adic field whose Néron model would have a given connected commutative unipotent group as the identity component of its special fibre.