Bounds on Injective Dimension and Exceptional Complete Intersection Maps

Hossein Faridian

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arXiv · 2307.13121

Bounds on Injective Dimension and Exceptional Complete Intersection Maps

Hossein Faridian

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Abstract

We prove that if $f:R \rightarrow S$ is a local homomorphism of noetherian local rings, and $M$ is a non-zero finitely generated or artinian $S$-module whose injective dimension over $R$ is bounded by the difference of the embedding dimensions of $R$ and $S$, then $M$ is an injective $S$-module and $f$ is an exceptional complete intersection map.

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Hossein Faridian. 2023-07-24. Bounds on Injective Dimension and Exceptional Complete Intersection Maps. https://arxiv.org/abs/2307.13121

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