In this paper, we prove that a weak form of the Akizuki–Nakano vanishing theorem holds on singular globally F-split 3-folds. Making use of this vanishing theorem, we study deformations of globally F-split Fano 3-folds and the Kodaira vanishing theorem for thickenings of locally complete intersection globally F-regular 3-folds.

中文翻译：

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奇异全局 F 分裂 3 倍的弱 Akizuki-Nakano 消失定理

在本文中，我们证明了 Akizuki-Nakano 消失定理的弱形式在奇异全局F分裂 3 倍上成立。利用这个消失定理，我们研究了全局F分裂 Fano 3 倍的变形和局部完全交集加厚的 Kodaira 消失定理全局F正则 3 倍。