Cohomologically complete intersections with vanishing of Betti numbers

Abstract

Let $I$ be ideal of an $n$-dimensional local Gorenstein ring $R$. In this paper we will describe several necessary and sufficient conditions such that the ideal $I$ becomes cohomologically complete intersections. In fact, as a technical tool, it will be shown that the vanishing $H_I^i(R)=0$ for all $i\neq c= \grade (I)$ is equivalent to the vanishing of the Betti numbers of $H_I^c(R)$. This gives a new characterization to check the cohomologically complete intersections property with the homological properties of the vanishing of Tor modules of $H_I^c(R)$.

submitted

References in corpus (1)

• Local Cohomology and Matlis duality