Localization, local cohomology, and the b-function of a D-module with respect to a polynomial
Localization, local cohomology, and the b-function of a D-module with respect to a polynomial
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DOI：
10.2969/aspm/07710353
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发表时间：
2016-09
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通讯作者：
T. Oaku
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文献类型：
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作者：
T. Oaku
给定一个由单个元素生成的$D$-模块$M$，和一个多项式$f$，可以构造几个$D$-模块附加在$M$和$f$上，并且可以定义M. Kashiwara之后的（广义的）$b$-函数的概念。这些模块与$M$的局部上同调和局部上同调密切相关。我们证明了$b$-函数（如果它存在）控制这些模块，并给出了计算这些模块和$b$-函数（如果它存在）的一般算法，而没有任何进一步的假设。对于这些算法，我们重新制定了D -模块的定位算法。
Given a $D$-module $M$ generated by a single element, and a polynomial $f$, one can construct several $D$-modules attached to $M$ and $f$ and can define the notion of the (generalized) $b$-function following M. Kashiwara. These modules are closely related to the localization and the local cohomology of $M$. We show that the $b$-function, if it exists, controls these modules and present general algorithms for computing these modules and the $b$-function (if it exists) without any further assumptions. For these algorithms, we reformulate the localization algorithm for $D$-modules.