The -invariant over splitting fields of Tits algebras

IF 1.3 1区数学 Q1 MATHEMATICS Compositio Mathematica Pub Date : 2024-09-11 DOI:10.1112/s0010437x24007255

Maksim Zhykhovich

引用次数: 0

Abstract

We describe the Abstract Image $J$-invariant of a semisimple algebraic group $G$ over a generic splitting field of a Tits algebra of $G$ in terms of the $J$-invariant over the base field. As a consequence we prove a 10-year-old conjecture of Quéguiner-Mathieu, Semenov, and Zainoulline on the $J$-invariant of groups of type Abstract Image $\mathrm {D}_n$. In the case of type $\mathrm {D}_n$ we also provide explicit formulas for the first component and in some cases for the second component of the $J$-invariant.

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蒂茨代数分裂域上的-不变量

我们用在基域上的 $J$ 不变式来描述在 $G$ 的 Tits 代数的一般分裂域上的半简代数群 $G$ 的 $J$ 不变式。因此，我们证明了奎吉纳-马蒂厄（Quéguiner-Mathieu）、塞梅诺夫（Semenov）和扎伊努林（Zainoulline）关于$\mathrm {D}_n$ 型群的$J$不变量的一个已有 10 年之久的猜想。在$\mathrm {D}_n$ 类型的情况下，我们还提供了$J$不变量第一分量的明确公式，在某些情况下还提供了第二分量的明确公式。

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

Compositio Mathematica 数学-数学

CiteScore

2.10

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Compositio Mathematica is a prestigious, well-established journal publishing first-class research papers that traditionally focus on the mainstream of pure mathematics. Compositio Mathematica has a broad scope which includes the fields of algebra, number theory, topology, algebraic and differential geometry and global analysis. Papers on other topics are welcome if they are of broad interest. All contributions are required to meet high standards of quality and originality. The Journal has an international editorial board reflected in the journal content.

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