Toward an efficient algorithm for deciding the vanishing of local cohomology modules in prime characteristic

Abstract

Let $$R=k[x_1,\dots ,x_n]$$ be a ring of polynomials over a field k of characteristic $$p>0$$ . There is an algorithm due to Lyubeznik for deciding the vanishing of local cohomology modules $$H^i_I(R)$$ where $$I\subset R$$ is an ideal. This algorithm has not been implemented because its complexity grows very rapidly with the growth of p which makes it impractical. In this paper we produce a modification of this algorithm that consumes a modest amount of memory.