$\mathbb{A}^1$ -同伦等价与Whitehead定理
$\mathbb{A}^1$-homotopy equivalences and a theorem of Whitehead
摘要：
我们证明类似物的怀特海定理（从代数拓扑）的周群和Grothendieck群的相干层：一个态射之间的光滑投射品种的推进是一个同构的周群，或对Grothendieck群的相干层，是一个同构。作为推论，我们证明了光滑射影簇之间不存在非平凡的朴素$\mathbb{A}^1$ -同伦等价。
英文摘要：
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.
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