When the base ring is not a field, power reductivity of a group scheme is a basic notion, intimately tied with finite generation of subrings of invariants. Geometric reductivity is weaker and less pertinent in this context. We give a survey of these properties and their connections.

中文翻译：

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仿射基上的还原性

当基环不是域时，群方案的幂还原性是一个基本概念，与不变量子环的有限生成密切相关。在这种情况下，几何还原性较弱且相关性较低。我们对这些属性及其联系进行了调查。