Higher direct images of the structure sheaf in positive characteristic
Higher direct images of the structure sheaf in positive characteristic
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DOI：
10.2140/ant.2011.5.693
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发表时间：
2009-11
期刊：
影响因子：
--
通讯作者：
A. Chatzistamatiou;Kay Rulling
中科院分区：
文献类型：
--
作者：
A. Chatzistamatiou;Kay Rulling
我们证明了消失的结构（和规范）层的高直接图像的一个适当的双有理态射与源的光滑品种和目标的商的光滑品种的有限群的阶素的地面字段的特点。我们还表明，光滑的投射品种的结构层的上同调是一个双有理不变量。这些结果在特征零点中是众所周知的。
We prove vanishing of the higher direct images of the structure (and the canonical) sheaf for a proper birational morphism with source a smooth variety and target the quotient of a smooth variety by a finite group of order prime to the characteristic of the ground field. We also show that for smooth projective varieties the cohomology of the structure sheaf is a birational invariant. These results are well-known in characteristic zero.