Nagoya Mathematical Journal
- Nagoya Math. J.
- Volume 217 (2015), 1-21.
de Rham cohomology of local cohomology modules: The graded case
Let be a field of characteristic zero, and let . Let be the th Weyl algebra over . We consider the case when and are graded by giving and for (here are positive integers). Set . Let be a graded ideal in . By a result due to Lyubeznik the local cohomology modules are holonomic -modules for each . In this article we prove that the de Rham cohomology modules are concentrated in degree ; that is, for . As an application when is an isolated singularity, we relate to , the th Koszul cohomology of with respect to .
Nagoya Math. J., Volume 217 (2015), 1-21.
First available in Project Euclid: 26 January 2015
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 13D45: Local cohomology [See also 14B15]
Secondary: 13N10: Rings of differential operators and their modules [See also 16S32, 32C38]
Puthenpurakal, Tony J. de Rham cohomology of local cohomology modules: The graded case. Nagoya Math. J. 217 (2015), 1--21. doi:10.1215/00277630-2857430. https://projecteuclid.org/euclid.nmj/1422282101