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arXiv · 2108.00204

Support Varieties and cohomology of Verdier quotients of stable category of complete intersection rings

Tony J. Puthenpurakal
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Abstract

Let $(A,\mathfrak{m})$ be a complete intersection with $k = A/\mathfrak{m}$ algebraically closed. Let CMS(A) be the stable category of maximal CM $A$-modules. For a large class of thick subcategories $\mathcal{S}$ of CMS(A) we show that there is a theory of support varieties for the Verdier quotient $\mathcal{T} = $ CMS(A)$/\mathcal{S}$. As an application we show that the analogous version of Auslander-Reiten conjecture, Murthys result, Avramov-Buchweitz result on symmetry of vanishing of cohomology holds for $\mathcal{T}$.

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Tony J. Puthenpurakal. 2021-07-31. Support Varieties and cohomology of Verdier quotients of stable category of complete intersection rings. https://arxiv.org/abs/2108.00204

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