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arXiv · 2307.15253

A categorical characterization of quantum projective $\mathbb Z$-spaces

Izuru Mori·Adam Nyman
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Abstract

In this paper, we study a generalization of the notion of AS-regularity for connected $\mathbb{Z}$-algebras. Our main result is a characterization of those categories equivalent to noncommutative projective schemes associated to right coherent regular $\mathbb{Z}$-algebras, which we call quantum projective $\mathbb{Z}$-spaces in this paper. As an application, we show that smooth quadric hypersurfaces and the standard noncommutative smooth quadric surfaces have right noetherian AS-regular $\mathbb{Z}$-algebras as homogeneous coordinate algebras. In particular, the latter are thus noncommutative $\mathbb{P}^1\times \mathbb{P}^1$.

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Izuru Mori, Adam Nyman. 2023-07-28. A categorical characterization of quantum projective $\mathbb Z$-spaces. https://arxiv.org/abs/2307.15253

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