论文标题
经典不变戒指上的差异操作员不提起模量$ p $
Differential operators on classical invariant rings do not lift modulo $p$
论文作者
论文摘要
Levasseur和Stafford在各种特征性零的古典环上描述了差异操作员的戒指；在他们考虑的每种情况下，差分运算符形成一个简单的环。为了对差异算子对副本数的不变环的不变环的攻击，史密斯和范·丹·伯格（Van den Bergh）询问差分运算符是否在相应的质量特征性升力的相应环上，特征性零差分运算符。我们证明，确定性超曲面以及PFAFFIAN和对称的确定性超曲面并非如此。我们还证明，除了极少数例外，这些超曲面 - 更一般而言，经典的不变环 - 不承认Frobenius内态性的mod $ p^2 $。
Levasseur and Stafford described the rings of differential operators on various classical invariant rings of characteristic zero; in each of the cases that they considered, the differential operators form a simple ring. Towards an attack on the simplicity of rings of differential operators on invariant rings of linearly reductive groups over the complex numbers, Smith and Van den Bergh asked if differential operators on the corresponding rings of positive prime characteristic lift to characteristic zero differential operators. We prove that, in general, this is not the case for determinantal hypersurfaces, as well as for Pfaffian and symmetric determinantal hypersurfaces. We also prove that, with very few exceptions, these hypersurfaces -- and, more generally, classical invariant rings -- do not admit a mod $p^2$ lift of the Frobenius endomorphism.
