Hodge-Witt decomposition of relative crystalline cohomology
Hodge-Witt decomposition of relative crystalline cohomology
复制标题
相对晶体上同调的 Hodge-Witt 分解
DOI：
10.1112/jlms.12679
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发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Gregory O
中科院分区：
文献类型：
--
作者：
Gregory O
对于在完全剩余域上具有普通约化的Artin局部环上的光滑和适当的方案，我们证明了-在一些一般假设下-相对的de Rham-Witt谱序列退化，并且相对的结晶上同调，配备了来自Nygaard复形的显示结构，具有Hodge-Witt分解为（适当地Tate-Twisted）乘法显示的直和。作为例子，我们的主要结果包括阿贝尔格式，完全相交，曲面，K3型簇和一些Calabi-Yau n$n$-folds的情况。
For a smooth and proper scheme over an Artinian local ring with ordinary reduction over the perfect residue field, we prove — under some general assumptions — that the relative de Rham–Witt spectral sequence degenerates and the relative crystalline cohomology, equipped with its display structure arising from the Nygaard complexes, has a Hodge–Witt decomposition into a direct sum of (suitably Tate‐Twisted) multiplicative displays. As examples, our main results include the cases of abelian schemes, complete intersections, surfaces, varieties of K3 type and some Calabi–Yau n$n$‐folds.