On derived functors of graded local cohomology modules-II

Abstract

Let $R=K[X_1,\dots ,X_n]$ where $K$ is a field of characteristic zero, and let $A_n(K)$ be the $n^{th}$ Weyl algebra over $K$. We give standard grading on $R$ and $A_n(K)$. Let $I$, $J$ be homogeneous ideals of $R$. Let $M=H_I^i(R)$ and $N=H_J^j(R)$ for some $i,j$. We show that $\Ext_{A_n(K)}^ν(M,N)$ is concentrated in degree zero for all $\nu \ge 0$, i.e., $\Ext_{A_n(K)}^ν(M,N)_l=0$ for $l\ne 0$. This proves a conjecture stated in part I of this paper.