In parts I and II, we determined which faithful irreducible representations V of a simple linear algebraic group G are generically free for Lie(G), i.e., which V have an open subset consisting of vectors whose stabilizer in Lie(G) is zero, with some assumptions on the characteristic of the field. This paper settles the remaining cases, which are of a different nature because Lie(G) has a more complicated structure and there need not exist general dimension bounds of the sort that exist in good characteristic.

中文翻译：

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普遍免费的陈述III：极端错误的特征

在第一部分和第二部分中，我们确定了简单线性代数组G的哪些忠实的不可约表示V对于Lie（G）通常是自由的，即哪个V具有由在Lie（G）中的稳定器为零的向量组成的开放子集，关于该领域的特征有一些假设。本文解决了其余情况，它们的性质不同，因为Lie（G）具有更复杂的结构，并且不需要存在具有良好特征的一般维数边界。