Coherent $I$-indexed algebras and noncommutative projective schemes

[2507.13828] Coherent $I$-indexed algebras and noncommutative projective schemes Skip to main content Search Submit Donate Log in Mathematics > Rings and Algebras arXiv:2507.13828 (math) [Submitted on 18 Jul 2025 ( v1 ), last revised 25 Aug 2026 (this version, v2)] Title: Coherent $I$-indexed algebras and noncommutative projective schemes Authors: Jackson Ryder View PDF HTML (experimental) 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. Comments: 26 pages. Substantial revision of Section 3, with smaller changes to Sections 4, 5 and 6. Section 7 added containing an application of the main result to the representation theory of bimodule species Subjects: Rings and Algebras (math.RA) ; Algebraic Geometry (math.AG) Cite as: arXiv:2507.13828 [math.RA] (or arXiv:2507.13828v2 [math.RA] for this version) https://doi.org/10.48550/arXiv.2507.13828 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Jackson Ryder [ view email ] [v1] Fri, 18 Jul 2025 11:36:24 UTC (17 KB) [v2] Tue, 25 Aug 2026 09:43:25 UTC (29 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.RA < prev | next > new | recent | 2025-07 Change to browse by: math math.AG References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from (opens in new tab) (opens in new tab) (opens in new tab)

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