Geodesic
Constructible $1$-Motives and Exactness of Realisation Functors
Documenta mathematica, Tome 24 (2019), pp. 1721-1737
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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.
DOI : 10.4171/dm/713
Classification : 14C15, 19E15
Mots-clés : Voevodsky motives, Deligne 1-motives, motivic t-structure 
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     author = {Simon Pepin Lehalleur},
     title = {Constructible $1${-Motives} and {Exactness} of {Realisation} {Functors}},
     journal = {Documenta mathematica},
     pages = {1721--1737},
     year = {2019},
     volume = {24},
     doi = {10.4171/dm/713},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/713/}
}
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Simon Pepin Lehalleur. Constructible $1$-Motives and Exactness of Realisation Functors. Documenta mathematica, Tome 24 (2019), pp. 1721-1737. doi: 10.4171/dm/713

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