Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quadratic Gorenstein rings and the Koszul property I   Let $R$ be a standard graded Gorenstein algebra over a field presented by
quadrics. Conca, Rossi, and Valla have shown that such a ring is Koszul if
$\mathrm{reg}\, R \leq 2$ or if $\mathrm{reg}\, = 3$ and $c= \mathrm{codim}\, R
\leq 4$, and they ask whether this is true for $\mathrm{reg}\, R = 3$ in
general. We determine sufficient conditions on a non-Koszul quadratic
Cohen-Macaulay ring $R$ that guarantee the Nagata idealization $\tilde{R} = R
\ltimes \omega_R(-a-1)$ is a non-Koszul quadratic Gorenstein ring. We use this
to negatively answer the question of Conca-Rossi-Valla, constructing non-Koszul
quadratic Gorenstein rings of regularity 3 for all $c \geq 9$.

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The categories of this paper are: hep-th
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The categories of this paper are: funct-an
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The categories of this paper are: stat
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The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat
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The categories of this paper are: q-alg