We show a vanishing result for the first direct image of a proper birational morphism of normal quasi-excellent schemes with regular codomain. As a consequence, we deduce the birational invariance of \(H^1(X,{\mathcal {O}}_X)\) for regular quasi-excellent schemes X. More generally, this is shown for quasi-excellent X which are \(S_3\) and pseudo-rational in codimension 2.

中文翻译：

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$$H^1({\mathcal {O}})$$ 的双有理不变性

我们展示了具有正则共域的正常准优秀方案的真双有理态射的第一个直接图像的消失结果。因此，我们推导出常规准优秀方案X的双有理不变性\(H^1(X,{\mathcal {O}}_X)\)。更一般地，这显示了准优秀X，它是\(S_3\)且在余维 2 中是伪有理数。