Detecting motivic equivalences with motivic homology

Proceedings of the American Mathematical Society, Series B Pub Date : 2020-12-04 DOI:10.1090/bproc/82

David Hemminger

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引用次数: 1

Abstract

Let k k be a field, let R R be a commutative ring, and assume the exponential characteristic of k k is invertible in R R . In this note, we prove that isomorphisms in Voevodsky’s triangulated category of motives D M ( k ; R ) \mathcal {DM}(k;R) are detected by motivic homology groups of base changes to all separable finitely generated field extensions of k k . It then follows from previous conservativity results that these motivic homology groups detect isomorphisms between certain spaces in the pointed motivic homotopy category H ( k ) ∗ \mathcal {H}(k)_* .

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用动机同源性检测动机等值

设k k是一个域，R R是一个交换环，并假设k k的指数特征在R R中是可逆的。在这篇笔记中，我们证明了Voevodsky的动机的三角范畴D M (k;R) \mathcal {DM}(k;R)由基变化的动机同调群检测到k k的所有可分离有限生成的域扩展。然后由先前的保守性结果得出，这些动机同伦群在点动机同伦范畴H (k)∗\mathcal {H}(k)_*中的某些空间之间检测到同构。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Proceedings of the American Mathematical Society, Series B

CiteScore

1.60

自引率

0.00%

发文量