Gauss-Manin connection via Witt-Differentials
Gauss-Manin connection via Witt-Differentials
复制标题
通过维特微分连接高斯-马宁
作者：
A. Langer;T. Zink
设X/R是环R上的光滑概型。考虑在Situs Crys（X/Wt（R））上有限秩的局部自由晶体范畴。我们证明了它等价于具有幂零可积的de Rham-Witt联络的有限秩局部自由模范畴。在R是完全域的情况下，Etesse [E]和Bloch [BI]证明了这一点。我们利用这个结果构造了Gauel-Manin联络作为de Rham-Witt联络。
Abstract Let X/R be a smooth scheme over a ring R. Consider the category of locally free crystals of finite rank on the situs Crys(X/Wt (R)). We show that it is equivalent to the category of locally free -modules of finite rank endowed with a nilpotent, integrable de Rham-Witt connection. In the case where R is a perfect field this was shown by Etesse [E] and Bloch [Bl]. We use the result for a construction of the Gauß-Manin connection as a de Rham-Witt connection.