Geodesic
$\mathbb{A}^1$-homotopy equivalences and a theorem of Whitehead
Homology, homotopy, and applications, Tome 23 (2021) no. 1, pp. 257-274.

Voir la notice de l'article provenant de la source International Press of Boston

We prove analogs of Whitehead’s theorem (from algebraic topology) for both the Chow groups and for the Grothendieck group of coherent sheaves: a morphism between smooth projective varieties whose pushforward is an isomorphism on the Chow groups, or on the Grothendieck group of coherent sheaves, is an isomorphism. As a corollary, we show that there are no nontrivial naive $\mathbb{A}^1$-homotopy equivalences between smooth projective varieties.
DOI : 10.4310/HHA.2021.v23.n1.a14
Classification : 14C25, 14C35
Keywords: Chow group, Grothendieck group, $\mathbb{A}^1$-homotopy 
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Eoin Mackall. $\mathbb{A}^1$-homotopy equivalences and a theorem of Whitehead. Homology, homotopy, and applications, Tome 23 (2021) no. 1, pp. 257-274. doi : 10.4310/HHA.2021.v23.n1.a14. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2021.v23.n1.a14/

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