On the descent for quadratic and bilinear forms

IF 0.8 3区数学 Q2 MATHEMATICS

Mathematische Nachrichten Pub Date : 2024-10-03 DOI:10.1002/mana.202400061

Ahmed Laghribi, Diksha Mukhija

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引用次数: 0

Abstract

This paper is devoted to the study of the descent problem in the spirit of conjectures proposed by Kahn in characteristic different from 2. The descent problem seeks conditions under which a $K$ -form (quadratic or bilinear) is defined over $F$ for a field extension $K / F$ . We study this problem in a complete manner for $K$ -quadratic and bilinear forms up to dimension 4 when $F$ is a field of characteristic 2 and $K$ is the function field of a projective quadric.

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关于二次和双线性形式的下降

本文以Kahn提出的不同于2的特征的猜想的精神来研究下降问题。下降问题寻求在F$ F$上为域扩展K/F$ K/F$定义K$ K$ -形式（二次或双线性）的条件。当F$ F$是特征为2的域，K$ K$是射影二次元的函数域时，我们完整地研究了K$ K$ -二次元和双线性到4维的问题。

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

Mathematische Nachrichten 数学-数学

CiteScore

1.50

自引率

0.00%

发文量

157

审稿时长

4-8 weeks

期刊介绍： Mathematische Nachrichten - Mathematical News publishes original papers on new results and methods that hold prospect for substantial progress in mathematics and its applications. All branches of analysis, algebra, number theory, geometry and topology, flow mechanics and theoretical aspects of stochastics are given special emphasis. Mathematische Nachrichten is indexed/abstracted in Current Contents/Physical, Chemical and Earth Sciences; Mathematical Review; Zentralblatt für Mathematik; Math Database on STN International, INSPEC; Science Citation Index