$\mathbb{A}^1$-homotopy equivalences and a theorem of Whitehead
Algebraic Geometry
2021-03-04 v1
Abstract
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 -homotopy equivalences between smooth projective varieties.
Keywords
Cite
@article{arxiv.2103.02204,
title = {$\mathbb{A}^1$-homotopy equivalences and a theorem of Whitehead},
author = {Eoin Mackall},
journal= {arXiv preprint arXiv:2103.02204},
year = {2021}
}