On the relative motive of a commutative group scheme

TL;DR

This paper establishes a canonical Künneth decomposition for the relative motive of a smooth commutative group scheme over a noetherian base, advancing the understanding of motives in algebraic geometry.

Contribution

It introduces a canonical Künneth decomposition for the relative motive of smooth commutative group schemes, extending previous work on motives of algebraic groups.

Findings

Canonical Künneth decomposition proven for relative motives

Extension of motive theory to smooth commutative group schemes

Provides a framework for analyzing motives over noetherian bases

Abstract

We prove a canonical Kuenneth decomposition of the relative motive with rational coefficients of a smooth commutative group scheme over a noetherian finite dimensional base. This paper is a follow-up of "On the motive of a commutative algebraic group" arXiv:1312.4171