$Z/p^2$上的全$p$ -差分
Total $p$-differentials on schemes over $Z/p^2$
摘要：
对于定义在特征$p$域的长度$2$ $p$ -典型Witt向量$W_2(k)$上的方案$X$，我们引入了全$p$ -微分，它插值于Frobenius-扭微分和Buium的$p$ -微分之间.它们在约化$X_0$上形成一个层，并且表现得好像它们是在$W_2(k)$下面的更深基上的$X$的微分层。这使我们能够构造高斯-马宁连接和Kodaira-Spencer类的类似物，就像Katz-Oda形式主义一样。我们连接到Frobenius电梯，博格-威兰的biring形式主义，和Deligne-Illusie类。
英文摘要：
For a scheme $X$ defined over the length $2$ $p$-typical Witt vectors $W_2(k)$ of a characteristic $p$ field, we introduce total $p$-differentials which interpolate between Frobenius-twisted differentials and Buium's $p$-differentials. They form a sheaf over the reduction $X_0$, and behave as if they were the sheaf of differentials of $X$ over a deeper base below $W_2(k)$. This allows us to construct the analogues of Gauss-Manin connections and Kodaira-Spencer classes as in the Katz-Oda formalism. We make connections to Frobenius lifts, Borger-Weiland's biring formalism, and Deligne--Illusie classes.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
