Geodesic
On the zeroth stable $\mathbb A^1$-homotopy group of a smooth projective variety
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 29, Tome 443 (2016), pp. 5-8 
A. S. Ananyevskiy. On the zeroth stable $\mathbb A^1$-homotopy group of a smooth projective variety. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 29, Tome 443 (2016), pp. 5-8. http://geodesic.mathdoc.fr/item/ZNSL_2016_443_a0/
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The zeroth stable $\mathbb A^1$-homotopy group of a smooth projective variety is computed. This group is identified with the group of oriented zero-cycles on the variety. The proof heavily exploits properties of strictly homotopy invariant sheaves.

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