任意域上的中间雅可比矩阵和合理性

IF 1.3 1区数学 Q1 MATHEMATICS

Annales Scientifiques De L Ecole Normale Superieure Pub Date : 2023-10-03 DOI:10.24033/asens.2549

Olivier Benoist, Olivier Wittenberg

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引用次数: 2

摘要

我们证明了两个二次曲面在域k上的三维光滑完全相交当且仅当它包含一条定义在k上的直线是k有理的。为此，我们发展了一个在任意，不一定是完美的域上的几何有理三折的中间雅可比矩阵理论。因此，我们得到了域k上具有k点的光滑射影变数的第一个例子，它们在k的纯不可分域扩展上是有理的，但不是在k上。

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Intermediate Jacobians and rationality over arbitrary fields

We prove that a three-dimensional smooth complete intersection of two quadrics over a field k is k-rational if and only if it contains a line defined over k. To do so, we develop a theory of intermediate Jacobians for geometrically rational threefolds over arbitrary, not necessarily perfect, fields. As a consequence, we obtain the first examples of smooth projective varieties over a field k which have a k-point, and are rational over a purely inseparable field extension of k, but not over k.

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来源期刊

Annales Scientifiques De L Ecole Normale Superieure 数学-数学

CiteScore

3.00

自引率

5.30%

发文量

审稿时长

>12 weeks

期刊介绍： The Annales scientifiques de l''École normale supérieure were founded in 1864 by Louis Pasteur. The journal dealt with subjects touching on Physics, Chemistry and Natural Sciences. Around the turn of the century, it was decided that the journal should be devoted to Mathematics. Today, the Annales are open to all fields of mathematics. The Editorial Board, with the help of referees, selects articles which are mathematically very substantial. The Journal insists on maintaining a tradition of clarity and rigour in the exposition. The Annales scientifiques de l''École normale supérieures have been published by Gauthier-Villars unto 1997, then by Elsevier from 1999 to 2007. Since January 2008, they are published by the Société Mathématique de France.