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# Nori motives of curves with modulus and Laumon $1$-motives

• Florian Ivorra,
Institut de recherche mathématique de Rennes , UMR 6625 du CNRS, Université de Rennes 1, Campus de Beaulieu, 35042 Rennes cedex (France)
• Takao Yamazaki,
Institute of mathematics , Tohoku University, Aoba, Sendaï, 980-8578 (Japan)
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## 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 $H^1_\mathrm{dR}$ 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.
 Keywords: motive, curve with modulus, quiver representation
 MSC Classifications: 19E15 - Algebraic cycles and motivic cohomology [See also 14C25, 14C35, 14F42] 16G20 - Representations of quivers and partially ordered sets 14F42 - Motivic cohomology; motivic homotopy theory [See also 19E15]

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