非闭合场上的Clemens-Griffiths方法

IF 1.2 1区数学 Q1 MATHEMATICS

Algebraic Geometry Pub Date : 2019-03-19 DOI:10.14231/AG-2020-025

Olivier Benoist, Olivier Benoist, Olivier Wittenberg, Olivier Wittenberg

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引用次数: 21

摘要

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。

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The Clemens–Griffiths method over non-closed fields

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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来源期刊

Algebraic Geometry Mathematics-Geometry and Topology

CiteScore

2.40

自引率

0.00%

发文量

审稿时长

52 weeks

期刊介绍： This journal is an open access journal owned by the Foundation Compositio Mathematica. The purpose of the journal is to publish first-class research papers in algebraic geometry and related fields. All contributions are required to meet high standards of quality and originality and are carefully screened by experts in the field.