Singularity Categories of Simple Singularities in Positive Characteristic

[2608.27738] Singularity Categories of Simple Singularities in Positive Characteristic Skip to main content Search Submit Donate Log in Mathematics > Algebraic Geometry arXiv:2608.27738 (math) [Submitted on 27 Aug 2026] Title: Singularity Categories of Simple Singularities in Positive Characteristic Authors: Yuta Takashima View PDF Abstract: We study the singularity categories of simple singularities of the same dimension over an algebraically closed field of positive characteristic, and show that, as in characteristic zero, these categories are not equivalent as triangulated categories unless the underlying singularities are analytically isomorphic. In contrast to the characteristic zero case, simple singularities in positive characteristic cannot be distinguished solely from the Auslander-Reiten quivers of their singularity categories. To address this, we extend to positive characteristics a theorem by Hua and Keller, which asserts that the 0th Hochschild cohomology of the dg singularity category of an isolated hypersurface singularity in characteristic zero is isomorphic to the Tyurina algebra of the defining polynomial. Furthermore as an application, we determine the condition for the singularity category of a rational double point (i.e., a simple singularity of dimension two) to be standard. We prove that such a category is standard if and only if the defining polynomial is weighted homogeneous. Subjects: Algebraic Geometry (math.AG) ; Category Theory (math.CT); Representation Theory (math.RT) MSC classes: 14F08, 14B05, 13D03 Cite as: arXiv:2608.27738 [math.AG] (or arXiv:2608.27738v1 [math.AG] for this version) https://doi.org/10.48550/arXiv.2608.27738 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Yuta Takashima [ view email ] [v1] Thu, 27 Aug 2026 21:55:23 UTC (22 KB) Full-text links: Access Paper: View PDF TeX Source view license Current browse context: math.AG < prev | next > new | recent | 2026-08 Change to browse by: math math.CT math.RT 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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