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arXiv · 2601.20596

Annihilator of $Ext^i_R(R/I,R)$

Mohsen Asgharzadeh
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Abstract

We investigate the higher divisorial ideal $D(I) := Ann(Ext^g_R(R/I,R))$ associated to an ideal $I$ of grade $g$. Our main focus is the containment problem $ D(I) \subseteq \overline{I}$. We show that this inclusion holds for broad classes of ideals, including unmixed ideals of finite projective dimension over $3$-dimensional quasi-normal rings, parameter ideals in quasi-Gorenstein rings, and powers of perfect ideals under suitable homological conditions. Conversely, we construct explicit examples demonstrating the necessity of these hypotheses. We develop structural properties of $D(I)$, relating it to unmixed parts, reflexive closures, symbolic powers, Frobenius closure, and trace ideals. Applications include the rigidity property of homological annihilators, a criteria for the triviality of reflexive modules and vector bundles on punctured spectra, as well as new connections among annihilators of Ext, conductor ideals, and local cohomology.

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Mohsen Asgharzadeh. 2026-09-03. Annihilator of $Ext^i_R(R/I,R)$. https://arxiv.org/abs/2601.20596

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