We establish structure results for Frobenius kernels of automorphism group schemes for surfaces of general type in positive characteristic. It turns out that there are surprisingly few possibilities. This relies on properties of the famous Witt algebra, which is a simple Lie algebra without finite-dimensional counterpart over the complex numbers, together with its twisted forms. The result actually holds true for arbitrary proper integral schemes under the assumption that the Frobenius kernel has large isotropy group at the generic point. This property is measured by a new numerical invariant called the foliation rank.

中文翻译：

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自同构群方案的 Frobenius 核的结构

我们建立了正特征一般类型曲面自同构群方案的 Frobenius 核的结构结果。事实证明，可能性出奇地少。这依赖于著名的维特代数的性质，它是一个简单的李代数，没有复数的有限维对应物及其扭曲形式。假设 Frobenius 核在泛点处具有大的各向同性群，该结果实际上适用于任意真积分方案。该属性通过称为叶状排列的新数值不变量来测量。