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arXiv · 1609.04676

Localization, local cohomology, and the b-function of a D-module with respect to a polynomial

Toshinori Oaku
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Abstract

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.

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Toshinori Oaku. 2016-09-15. Localization, local cohomology, and the b-function of a D-module with respect to a polynomial. https://arxiv.org/abs/1609.04676

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