Nori motives of curves with modulus and Laumon 1-motives

TL;DR

This paper characterizes Laumon 1-isomotives over a number field as a universal Nori category derived from smooth proper curves with divisors, extending previous work on 1-motives and motives.

Contribution

It introduces a new description of Laumon 1-isomotives via Nori's framework, connecting curves with modulus and de Rham cohomology to the theory of motives.

Findings

Provides a universal category for Laumon 1-isomotives based on a quiver representation.

Extends the theorem of Ayoub and Barbieri-Viale to include curves with modulus.

Links 1-isomotives to Nori's category of motives through explicit geometric data.

Abstract

Let $k$ be a number field. We describe the category of Laumon 1-isomotives over $k$ as the universal category in the sense of Nori associated with a quiver representation built out of smooth proper $k$-curves with two disjoint effective divisors and a notion of $H^1_\dR$ for such "curves with modulus". This result extends and relies on the theorem of J. Ayoub and L. Barbieri-Viale that describes Deligne's category of 1-isomotives in terms of Nori's Abelian category of motives.