The Clemens–Griffiths method over non-closed fields

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2019-03-19 DOI:10.14231/AG-2020-025

Olivier Benoist, Olivier Benoist, Olivier Wittenberg, Olivier Wittenberg

引用次数: 21

Abstract

We use the Clemens-Griffiths method to construct smooth projective threefolds, over any field $k$ admitting a separable quadratic extension, that are $k$-unirational and $\bar{k}$-rational but not $k$-rational. When $k=\mathbb{R}$, we can moreover ensure that their real locus is diffeomorphic to the real locus of a smooth projective $\mathbb{R}$-rational variety and that all their unramified cohomology groups are trivial.

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非闭合场上的Clemens-Griffiths方法

我们利用Clemens-Griffiths方法构造了在允许可分二次扩展的任意域$k$上，$k$-酉和$\bar{k}$-有理但不是$k$-有理的光滑投影三倍。当$k=\mathbb{R}$时，我们还可以保证它们的实轨迹与光滑射影$\mathbb{R}$的实轨迹是微分同态的，并且它们的所有未分枝上同调群都是平凡的。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.