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arXiv · 2101.12287

Support varieties over skew complete intersections via derived braided Hochschild cohomology

Luigi Ferraro·W. Frank Moore·Josh Pollitz
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Abstract

In this article we study a theory of support varieties over a skew complete intersection $R$, i.e. a skew polynomial ring modulo an ideal generated by a sequence of regular normal elements. We compute the derived braided Hochschild cohomology of $R$ relative to the skew polynomial ring and show its action on $\mathrm{Ext}_R(M,N)$ is noetherian for finitely generated $R$-modules $M$ and $N$ respecting the braiding of $R$. When the parameters defining the skew polynomial ring are roots of unity we use this action to define a support theory. In this setting applications include a proof of the Generalized Auslander-Reiten Conjecture and that $R$ possesses symmetric complexity.

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BibTeXRIS

Luigi Ferraro, W. Frank Moore, Josh Pollitz. 2021-01-28. Support varieties over skew complete intersections via derived braided Hochschild cohomology. https://arxiv.org/abs/2101.12287

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