Generic elements of a Zariski-dense subgroup form an open subset
Generic elements of a Zariski-dense subgroup form an open subset
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Zariski 密集子群的通用元素形成开子集
DOI：
10.1090/mosc/274
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
A. Rapinchuk
中科院分区：
文献类型：
--
作者：
Gopal Prasad;A. Rapinchuk
设G是特征为零的广义生成域K上的半单代数群，\Gamma < G（K）是广义生成的Zakki稠密子群.本文证明了\Gamma的K-泛元集（其存在性已在[9]中建立）在\Gamma的profinite拓扑中是开的。然后我们将这个结果推广到正特征域，并证明了在这种情况下类属元的存在性。
Let G be a semi-simple algebraic group over a finitely generated field K of characteristic zero, and let \Gamma < G(K) be a finitely generated Zariski-dense subgroup. In this note we prove that the set of K-generic elements of \Gamma (whose existence was established earlier in [9]) is open in the profinite topology of \Gamma. We then extend this result to the fields of positive characteristic, and also prove the existence of generic elements in this case.