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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.13828 |
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| _version_ | 1866916849881448448 |
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| author | Ryder, Jackson |
| author_facet | Ryder, Jackson |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_13828 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Coherent $I$-indexed algebras and noncommutative projective schemes Ryder, Jackson Rings and Algebras Algebraic Geometry 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. |
| title | Coherent $I$-indexed algebras and noncommutative projective schemes |
| topic | Rings and Algebras Algebraic Geometry |
| url | https://arxiv.org/abs/2507.13828 |