论文标题
通过卡地亚操作员的差异表格的扩展性
Extendability of differential forms via Cartier operators
论文作者
论文摘要
让$ x $成为一个正常的积极特征和$ b $ a $ x $的除数的普通品种。我们证明，如果$（x，b）$的日志平滑基因座上的卡地亚同构扩展到整个$ x $，则$（x，b）$满足差分形式的对数扩展定理。作为应用程序，我们表明，对数扩展定理可以通过减少线性还原的组方案的作用来获得光滑品种的良好商。此外，在对Serre的状况的假设下，单一形式的对数扩展定理具有较高的编成性奇异性。我们还证明，驯服的商满足常规扩展定理。
Let $X$ be a normal variety over a perfect field of positive characteristic and $B$ a reduced divisor on $X$. We prove that if the Cartier isomorphism on the log smooth locus of $(X,B)$ extends to the entire $X$, then $(X,B)$ satisfies the logarithmic extension theorem for differential forms. As an application, we show that the logarithmic extension theorem holds for good quotients of smooth varieties by actions of reduced linearly reductive group schemes. In addition, the logarithmic extension theorem for one-forms holds for singularities of higher codimension under assumptions about Serre's condition. We also prove that tame quotients satisfy the regular extension theorem.
