Geodesic
Constructible $1$-Motives and Exactness of Realisation Functors
Documenta mathematica, Tome 24 (2019), pp. 1721-1737.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

The triangulated category of cohomological $1$-motives with rational coefficients over a base scheme admits a motivic t-structure. We prove that this t-structure restricts to the subcategory of compact objects, and that pullbacks along arbitrary morphisms, as well as Betti and étale realisation functors, are t-exact relative to this t-structure. These exactness properties follow from a structural result: compact objects in the heart behave like a constructible sheaf of Deligne $1$-motives.
Classification : 14C15, 19E15
Keywords: Voevodsky motives, Deligne \(1\)-motives, motivic t-structure 
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     author = {Lehalleur, Simon Pepin},
     title = {Constructible {\(1\)-Motives} and {Exactness} of {Realisation} {Functors}},
     journal = {Documenta mathematica},
     pages = {1721--1737},
     publisher = {mathdoc},
     volume = {24},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2019__24__a22/}
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Lehalleur, Simon Pepin. Constructible \(1\)-Motives and Exactness of Realisation Functors. Documenta mathematica, Tome 24 (2019), pp. 1721-1737. http://geodesic.mathdoc.fr/item/DOCMA_2019__24__a22/