We study the possible structures of monodromy groups of Kloosterman and hypergeometric sheaves on \({{\mathbb {G}}}_m\) in characteristic p. We show that most such sheaves satisfy a certain condition \(\mathrm {(\mathbf{S+})}\), which has very strong consequences on their monodromy groups. We also classify the finite, almost quasisimple, groups that can occur as monodromy groups of Kloosterman and hypergeometric sheaves.

中文翻译：

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Kloosterman 和超几何滑轮的单调群

我们在特征p 中研究了\({{\mathbb {G}}}_m\)上 Kloosterman 和超几何滑轮的单调群的可能结构。我们表明，大多数这样的滑轮满足某个条件\(\mathrm {(\mathbf{S+})}\)，这对它们的单向群有非常强烈的影响。我们还将可能出现的有限的、几乎准简单的群分类为 Kloosterman 和超几何滑轮的单调群。