Biextensions of 1-motives in Voevodsky's category of motives

TL;DR

This paper demonstrates that biextensions of 1-motives correspond to multilinear morphisms within Voevodsky's category of motives, establishing a new link between these concepts in algebraic geometry.

Contribution

It proves that biextensions of 1-motives induce multilinear morphisms in Voevodsky's triangulated category, connecting biextensions with the structure of motives.

Findings

Biextensions define multilinear morphisms in Voevodsky's motives

Establishes a new relationship between 1-motives and Voevodsky's category

Advances understanding of the structure of motives in algebraic geometry

Abstract

Let k be a perfect field. In this paper we prove that biextensions of 1-motives define multilinear morphisms between 1-motives in Voevodsky's triangulated category of effective geometrical motives over k with rational coefficients.