Algorithms for D-modules — restriction, tensor product, localization, and local cohomology groups

✍ Scribed by Toshinori Oaku; Nobuki Takayama

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 310 KB
• Volume: 156
• Category: Article
• ISSN: 0022-4049
• DOI: 10.1016/s0022-4049(00)00004-9

✦ Synopsis

We consider an algebraic D-module M on the a ne space, i.e. a system of linear partial di erential equations with polynomial coe cients. We give an algorithm for computing the cohomology groups of the restriction of M to a linear subvariety by using a free resolution of M adapted to the V -ÿltration. Our algorithm works, at least, if M is holonomic. As applications, we obtain algorithms for computing tensor product, localization, and algebraic local cohomology groups of holonomic systems.