Abstract
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 .
Citation
Tony J. Puthenpurakal. "de Rham cohomology of local cohomology modules: The graded case." Nagoya Math. J. 217 1 - 21, March 2015. https://doi.org/10.1215/00277630-2857430
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