Neron models for semiabelian varieties: Congruence and change of base field

Abstract

Let O be a henselian discrete valuation ring with perfect residue field. Denote by K the fraction field of O = OK , and by p = pK the maximal ideal of O. Then every abelian variety A over K has a Neron model A over O. The Neron model A of A is a smooth group scheme of finite type over O, characterized by the property that for every finite unramified extension L of K, every L-valued point of AK extends uniquely to an OL-valued point of A. We refer to the book [BLR] for a thorough exposition of the construction and basic properties of Neron models. In general, the formation of Neron models does not commute with base change. Rather, for every finite extension field M of K, we have a canonical homomorphism