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arXiv · 1610.00525

Linearity defect of the residue field of short local rings

Rasoul Ahangari Maleki
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Abstract

Let $(R,\m,k)$ be a Noetherian local ring with maximal ideal $\m$ and residue field $k$. The linearity defect of a finitely generated $R$-module $M$, which is denoted $\ld_R(M)$, is a numerical measure of how far $M$ is from having linear resolution. We study the linearity defect of the residue field. We give a positive answer to the question raised by Herzog and Iyengar of whether $\ld_R(k)<\infty$ implies $\ld_R(k)=0$, in the case when $\m^4=0$.

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Rasoul Ahangari Maleki. 2016-10-03. Linearity defect of the residue field of short local rings. https://arxiv.org/abs/1610.00525

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