On completion of graded $D$-modules
On completion of graded $D$-modules
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完成分级的 $D$ 模块后
DOI：
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发表时间：
2018
影响因子：
1
通讯作者：
Wenliang Zhang
中科院分区：
文献类型：
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作者：
N. Switala;Wenliang Zhang
设$R = k[x_1, ldots, x_n]$是特征为零的域$k$上的多项式环，$cR$是形式幂级数环$k[[x_1, ldots, x_n]]$。如果$M$是$D$-模比$R$，那么$cR otimes_R M$自然是$D$-模比$cR$。Hartshorne和Polini提出，当$M$被分级和完整时，$H^i_{dR}(M)到$H^i_{dR}(cR otimes_R M)$的自然映射$H^i_{dR}(cR otimes_R M$) $是否同构。我们对他们的问题给出一个肯定的答案，作为以下更有力结果的必然结果。设$M$是一个有限生成的分级$D$-模：对于每一个整数$i$使得$dim_kH^i_{dR}(M)< inty $，则自然映射$H^i_{dR}(M)到H^i_{dR}(cR otimes_R M)$（由$M到cR otimes_R M$导出）是同构的。
Let $R = k[x_1, ldots, x_n]$ be a polynomial ring over a field $k$ of characteristic zero and $cR$ be the formal power series ring $k[[x_1, ldots, x_n]]$. If $M$ is a $D$-module over $R$, then $cR otimes_R M$ is naturally a $D$-module over $cR$. Hartshorne and Polini asked whether the natural maps $H^i_{dR}(M) o H^i_{dR}(cR otimes_R M)$ (induced by $M o cR otimes_R M$) are isomorphisms whenever $M$ is graded and holonomic. We give a positive answer to their question, as a corollary of the following stronger result. Let $M$ be a finitely generated graded $D$-module: for each integer $i$ such that $dim_kH^i_{dR}(M)<infty$, the natural map $H^i_{dR}(M) o H^i_{dR}(cR otimes_R M)$ (induced by $M o cR otimes_R M$) is an isomorphism.
影响因子：
1.7
作者：
N. Switala;Wenliang Zhang
通讯作者：
N. Switala;Wenliang Zhang