半单代数群的母题等价
代数几何
2015-07-19 v1
摘要
两个半单代数群被称为母题等价的，如果相关联的广义旗流形的母题在任意素数p下均同构。本文的目的是构造刻画母题等价的组合不变量，它们是出现在半单代数群分类中的蒂茨指标的母题类似物。这些不变量——上蒂茨p指标——用与半单代数群的自然底层结构相关联的经典不变量来表达，从而能够产生母题等价的代数判据，推广了二次型的维希克母题等价判据。这也澄清了母题与广义旗流形的有理几何之间的关系。
引用
@article{arxiv.1507.04384,
title = {Equivalence motivique des groupes algebriques semisimples},
author = {Charles De Clercq},
journal= {arXiv preprint arXiv:1507.04384},
year = {2015}
}
备注
in French. The article refers several times to the determination of the Tits p-indexes of absolutely simple groups, which is contained in the article "On the Tits p-indexes of semisimple algebraic groups" (joint with Skip Garibaldi). A draft of this article (whose motivic part is not yet filled) is available on http://www.math.univ-paris13.fr/~declercq/ as well as an abridged english version of the article