Higher Displays Arising from Filtered de Rham–Witt Complexes
Higher Displays Arising from Filtered de Rham–Witt Complexes
复制标题
过滤后的 de Rham-Witt 复合物带来更高的显示效果
DOI：
10.1007/978-3-030-65203-6_5
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
A. Langer
中科院分区：
文献类型：
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作者：
Oliver Gregory;A. Langer
对于满足一般性假设的环R上的光滑投影概型X，证明了其晶上同调具有更高的显示结构，这是方丹强可除格的相对形式. Frobenius整除性是由相对的de Rham-Witt复形上的Nygaard滤子引起的。对于一个幂零的PD增厚$S/R$，我们还考虑了相关的相对显示，并可以明确地描述它的一个相对版本的Nygaard过滤的de Rham-Witt复杂的提升$X$超过$S$。证明了如果X的mod p约化具有光滑的变形空间，则存在相对显示的晶体.
For a smooth projective scheme $X$ over a ring $R$ on which $p$ is nilpotent that meets some general assumptions we prove that the crystalline cohomology is equipped with the structure of a higher display which is a relative version of Fontaine's strongly divisible lattices. Frobenius-divisibilty is induced by the Nygaard filtration on the relative de Rham-Witt complex. For a nilpotent PD-thickening $S/R$ we also consider the associated relative display and can describe it explicitly by a relative version of the Nygaard filtration on the de Rham-Witt complex associated to a lifting of $X$ over $S$. We prove that there is a crystal of relative displays if moreover the mod $p$ reduction of $X$ has a smooth and versal deformation space.