Multilinear morphisms between 1-motives

Abstract

We introduce the notion of biextensions of 1-motives over an arbitrary scheme S and we define bilinear morphisms between I-motives as isomorphism classes of such biextensions. If S is the spectrum of a field of characteristic 0, we check that these biextensions define bilinear morphisms between the realizations of 1-motives. Generalizing we obtain the notion of multilinear morphisms between 1-motives.