ON EXTENSIONS OF ALGEBRAIC GROUPS WITH FINITE QUOTIENT

被引：16
作者：
Brion, Michel [1 ]
机构：
[1] Univ Grenoble 1, Inst Fourier, 100 Rue Math, F-38402 St Martin Dheres, France
来源：
PACIFIC JOURNAL OF MATHEMATICS | 2015年 / 279卷 / 1-2期
关键词：
algebraic groups; finite quotients; extensions; equivariant compactifications;
D O I：
10.2140/pjm.2015.279.135
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Consider an exact sequence of group schemes of finite type over a field k, 1 -> N -> G -> Q -> 1, where Q is finite. We show that Q lifts to a finite subgroup scheme F of G; if Q is etale and k is perfect, then F may be chosen etale as well. As applications, we obtain generalizations of classical results of Arima, Chevalley, and Rosenlicht to possibly nonconnected algebraic groups. We also show that every homogeneous space under such a group has a projective equivariant compactification.
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页码：135 / 153
页数：19
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