$\mathbb｛A｝^1$-同胚等价与Whitehead的一个定理

IF 0.8 4区数学 Q2 MATHEMATICS

Homology Homotopy and Applications Pub Date : 2021-03-03 DOI:10.4310/HHA.2021.v23.n1.a14

Eoin Mackall

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引用次数: 0

摘要

我们证明了Whitehead定理（来自代数拓扑）对于Chow群和相干槽轮的Grothendieck群的相似性：光滑投影变体之间的态射，其前推是Chow群上的同构，或相干槽轮Grothendick群上的同态，是同构。作为一个推论，我们证明了在光滑射影变种之间不存在非平凡的天真a-同伦论等价。

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$\mathbb{A}^1$-homotopy equivalences and a theorem of Whitehead

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 A-homotopy equivalences between smooth projective varieties.

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来源期刊

Homology Homotopy and Applications 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Homology, Homotopy and Applications is a refereed journal which publishes high-quality papers in the general area of homotopy theory and algebraic topology, as well as applications of the ideas and results in this area. This means applications in the broadest possible sense, i.e. applications to other parts of mathematics such as number theory and algebraic geometry, as well as to areas outside of mathematics, such as computer science, physics, and statistics. Homotopy theory is also intended to be interpreted broadly, including algebraic K-theory, model categories, homotopy theory of varieties, etc. We particularly encourage innovative papers which point the way toward new applications of the subject.