Albanese varieties of singular varieties over a perfect field

TL;DR

This paper provides a functorial description of the Albanese variety for possibly singular projective varieties over perfect fields, extending previous constructions using duality theory of 1-motives.

Contribution

It introduces a new functorial framework for Albanese varieties of singular varieties over perfect fields, utilizing duality theory of 1-motives with unipotent parts.

Findings

Provides a functorial description of Albanese varieties over perfect fields

Extends previous constructions to singular varieties

Uses duality theory of 1-motives with unipotent parts

Abstract

Let X be a projective variety, possibly singular. A generalized Albanese variety of X was constructed by Esnault, Srinivas and Viehweg over algebraically closed base field as a universal regular quotient of the relative Chow group of 0-cycles by Levine-Weibel. In this paper, we obtain a functorial description of the Albanese of Esnault-Srinivas-Viehweg over a perfect base field, using duality theory of 1-motives with unipotent part.