Generalized 1-motivic sheaves

TL;DR

This paper extends the category of 1-motivic sheaves to include quotients involving formal groups and proves an equivalence of derived categories with generalized 1-motives, broadening the framework for motivic sheaves.

Contribution

It introduces a generalized category of 1-motivic sheaves incorporating formal group quotients and establishes a derived category equivalence with generalized 1-motives.

Findings

Extended 1-motivic sheaves to include formal group quotients.

Proved derived category equivalence with generalized 1-motives.

Broadened the theoretical framework for motivic sheaves.

Abstract

We extend the construction of the category of 1-motivic sheaves (introduced by Barbieri-Viale and Kahn) allowing quotients of connected algebraic k-groups by formal k-groups. We show that its bounded derived category is equivalent to the bounded derived category of the category of generalized 1-motives with torsion introduced in a previous paper by Barbieri-Viale and the author.