Biextensions of 1-motives in Voevodskys category of motives

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.

💡 Research Summary

**
The paper investigates the relationship between biextensions of Deligne’s 1‑motives and Voevodsky’s triangulated category of effective geometric motives (\mathbf{DM}^{\mathrm{eff}}{\mathrm{gm}}(k){\mathbb{Q}}) over a perfect field (k). A 1‑motive (M=