Motivic interpretation of Albanese varieties of smooth varieties

TL;DR

This paper introduces a derived Albanese construction for smooth schemes over algebraically closed fields within Voevodsky's motives, linking it to classical Albanese schemes and establishing its descent properties.

Contribution

It defines the derived Albanese in the context of Voevodsky's motives and relates it to existing Albanese schemes, expanding the theoretical framework.

Findings

Derived Albanese relates to classical Albanese schemes

Proves derived Albanese satisfies Nisnevich descent

Establishes a new motivic interpretation of Albanese varieties

Abstract

For every noetherian smooth and separated scheme over an algebraically closed field, we define its derived Albanese in Voevodsky's triangulated category of effective Nisnevich motives. To justify our definition, we relate the derived Albanese with the Albanese scheme. We also prove that the derived Albanese satisfies the Nisnevich descent property.