具有有限系数的高等周群与精制无ramified同调

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics Pub Date : 2024-10-15 DOI:10.1016/j.aim.2024.109972

Kees Kok , Lin Zhou

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引用次数: 0

摘要

在本文中，我们证明了布洛赫在一个域上的准投影等维方案的具有有限系数的高循环类映射自然地适合于涉及施赖埃德的精致无克拉姆同调的长精确序列。我们还证明了细化无克拉姆同调满足局部化序列。由此，我们最终猜想精炼无克拉姆同调是一种动机同调理论，并解释了这与上述结果的关系。

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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Higher Chow groups with finite coefficients and refined unramified cohomology

In this paper we show that Bloch's higher cycle class map with finite coefficients for quasi-projective equi-dimensional schemes over a field fits naturally in a long exact sequence involving Schreieder's refined unramified cohomology. We also show that the refined unramified cohomology satisfies the localization sequence. Using this we conjecture in the end that refined unramified cohomology is a motivic homology theory and explain how this is related to the aforementioned results.

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来源期刊

Advances in Mathematics 数学-数学

CiteScore

2.80

自引率

5.90%

发文量

497

审稿时长

7.5 months

期刊介绍： Emphasizing contributions that represent significant advances in all areas of pure mathematics, Advances in Mathematics provides research mathematicians with an effective medium for communicating important recent developments in their areas of specialization to colleagues and to scientists in related disciplines.