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arXiv · 2509.22988

Koszul cohomology and support of local cohomology modules of complete intersections

Michael Gintz·Wenliang Zhang
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Abstract

Let $R$ be a noetherian commutative ring and $f_1,\dots,f_c$ be a regular sequence in $R$. We introduce a framework to study $Supp(H^j_I(R/(f_1,\dots,f_c)))$ by linking the Koszul cohomology of $H^j_I(R)$ on the sequence $f_1,\dots,f_c$ and local cohomology modules $H^j_I(R/(f_1,\dots,f_c))$. As an application, we prove that if $R$ is a noetherian regular ring of prime characteristic $p$ and $f_1,f_2$ form a regular sequence in $R$ then $Supp(H^j_I(R/(f_1,f_2)))$ is Zariski-closed for each integer $j$ and each ideal $I$.

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Michael Gintz, Wenliang Zhang. 2025-09-26. Koszul cohomology and support of local cohomology modules of complete intersections. https://arxiv.org/abs/2509.22988

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