On derived functors of graded local cohomology modules—II

Abstract

Let R=K[X1,…,Xn], where K is a field of characteristic zero, and let An(K) be the nth Weyl algebra over K. We give standard grading on R and An(K). Let I, J be homogeneous ideals of R. Let M=HIi(R) and N=HJj(R) for some i,j. We show that ExtAn(K)ν(M,N) is concentrated in degree zero for all ν≥0 (i.e., ExtAn(K)ν(M,N)l=0 for l≠0). 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).