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arXiv · 2401.04987

Compactness of the Alexandrov topology of maximal Cohen-Macaulay modules

Kaito Kimura
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Abstract

Let $R$ be a Cohen-Macaulay local ring. In this paper, we first describe the radicals of annihilators of stable categories of maximal Cohen-Macaulay $R$-modules. We then prove that the Alexandrov topology of the stable category of maximal Cohen-Macaulay $R$-modules is compact provided that the completion of $R$ has an isolated singularity. Finally, we consider the case of a hypersurface of countable CM-representation type.

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Kaito Kimura. 2024-01-10. Compactness of the Alexandrov topology of maximal Cohen-Macaulay modules. https://arxiv.org/abs/2401.04987

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