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arXiv · 2301.01384

Dimension and depth inequalities over complete intersections

Petter Andreas Bergh·David A. Jorgensen·Peder Thompson
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Abstract

For a pair of finitely generated modules $M$ and $N$ over a codimension $c$ complete intersection ring $R$ with $\ell(M\otimes_RN)$ finite, we pay special attention to the inequality $\dim M+\dim N \leq \dim R +c$. In particular, we develop an extension of Hochster's theta invariant whose nonvanishing detects equality. In addition, we consider a parallel theory where dimension and codimension are replaced by depth and complexity, respectively.

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Petter Andreas Bergh, David A. Jorgensen, Peder Thompson. 2023-01-03. Dimension and depth inequalities over complete intersections. https://arxiv.org/abs/2301.01384

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