Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the linearity defect of the residue field   Given a commutative Noetherian local ring $R$, the linearity defect of a
finitely generated $R$-module $M$, denoted $\ld_R(M)$, is an invariant that
measures how far $M$ and its syzygies are from having a linear resolution.
Motivated by a positive known answer in the graded case, we study the question
of whether $\ld_R(k)<\infty$ implies $\ld_R(k)=0$. We give answers in special
cases, and we discuss several interpretations and refinements of the question.

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The categories of this paper are: hep-ph
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The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg
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The categories of this paper are: eess
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The categories of this paper are: cs
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph