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arXiv · 2507.13828

Coherent $I$-indexed algebras and noncommutative projective schemes

Jackson Ryder
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Abstract

We study coherent $I$-indexed algebras and associated noncommutative projective schemes, where the index set $I$ is a locally finite directed poset. Our main result is a characterisation of such noncommutative projective schemes in terms of sequences of objects with properties analogous to the sequence of tensor powers of an ample line bundle, extending a similar characterisation given by Polishchuk for coherent $\mathbb{Z}$-indexed algebras.

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Jackson Ryder. 2025-07-18. Coherent $I$-indexed algebras and noncommutative projective schemes. https://arxiv.org/abs/2507.13828

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