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

Yi Zhang

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arXiv · 1407.2583

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

Yi Zhang

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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.

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Yi Zhang. 2014-07-09. Toward an efficient algorithm for deciding the vanishing of local cohomology modules in prime characteristic. https://arxiv.org/abs/1407.2583

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