Annihilators of $D$-modules in mixed characteristic
Annihilators of $D$-modules in mixed characteristic
复制标题
混合特征的 $D$ 模块的歼灭者
DOI：
10.4310/mrl.2023.v30.n3.a5
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发表时间：
2019
影响因子：
1
通讯作者：
Wenliang Zhang
中科院分区：
文献类型：
--
作者：
Rankeya Datta;N. Switala;Wenliang Zhang
设$R$是多项式或形式幂级数环，其系数在具有均匀化子$\pi$的混合特征的DVR $V$中.我们证明了任何非零$\D（R，V）$-模的$R$-模零化子要么为零，要么由$\pi$的幂生成。与等特征情形相反，非零化子可以出现;我们给出一个环$\mathbb{Z}_2[[x_0，\ldots，x_5]]$的上局部上同调模被2 $零化的例子，从而回答了Hochster的一个否定问题。
Let $R$ be a polynomial or formal power series ring with coefficients in a DVR $V$ of mixed characteristic with a uniformizer $\pi$. We prove that the $R$-module annihilator of any nonzero $\D(R,V)$-module is either zero or is generated by a power of $\pi$. In contrast to the equicharacteristic case, nonzero annihilators can occur; we give an example of a top local cohomology module of the ring $\mathbb{Z}_2[[x_0, \ldots, x_5]]$ that is annihilated by $2$, thereby answering a question of Hochster in the negative.