Let , where is a field of characteristic zero, and let be the th Weyl algebra over . We give standard grading on and . Let , be homogeneous ideals of . Let and for some . We show that is concentrated in degree zero for all (i.e., for ). This proves a conjecture stated in Part I of this paper (T. J. Puthenpurakal and J. Singh, On derived functors of graded local cohomology modules, Math. Proc. Cambridge Philos. Soc. 167 (2018), no. 3, 549–565).
"On derived functors of graded local cohomology modules—II." Illinois J. Math. 64 (4) 595 - 612, December 2020. https://doi.org/10.1215/00192082-8720498