Essential dimension of the spin groups in characteristic 2

IF 1.1 3区数学 Q1 MATHEMATICS

Commentarii Mathematici Helvetici Pub Date : 2017-01-21 DOI:10.4171/CMH/452

B. Totaro

引用次数: 7

Abstract

We determine the essential dimension of the spin group Spin(n) as an algebraic group over a field of characteristic 2, for n at least 15. In this range, the essential dimension is the same as in characteristic not 2. In particular, it is exponential in n. This is surprising in that the essential dimension of the orthogonal groups is smaller in characteristic 2. We also find the essential dimension of Spin(n) in characteristic 2 for n at most 10.

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特征2中自旋群的本质维数

我们确定了自旋群spin（n）作为特征域2上的代数群的本质维数，对于n至少为15。在该范围内，基本尺寸与特征非2中的尺寸相同。特别地，它在n中是指数的。这令人惊讶，因为正交群的本质维数在特征2中较小。我们还在特征2中发现了Spin（n）的本质维度，对于n至多为10。

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

Commentarii Mathematici Helvetici 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Commentarii Mathematici Helvetici (CMH) was established on the occasion of a meeting of the Swiss Mathematical Society in May 1928. The first volume was published in 1929. The journal soon gained international reputation and is one of the world''s leading mathematical periodicals. Commentarii Mathematici Helvetici is covered in: Mathematical Reviews (MR), Current Mathematical Publications (CMP), MathSciNet, Zentralblatt für Mathematik, Zentralblatt MATH Database, Science Citation Index (SCI), Science Citation Index Expanded (SCIE), CompuMath Citation Index (CMCI), Current Contents/Physical, Chemical & Earth Sciences (CC/PC&ES), ISI Alerting Services, Journal Citation Reports/Science Edition, Web of Science.