[2306.14426] The Brauer-Manin obstruction on algebraic stacks Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Algebraic Geometry arXiv:2306.14426 (math) [Submitted on 26 Jun 2023 ( v1 ), last revised 30 Apr 2026 (this version, v3)] Title: The Brauer-Manin obstruction on algebraic stacks Authors: Chang Lv , Han Wu View a PDF of the paper titled The Brauer-Manin obstruction on algebraic stacks, by Chang Lv and Han Wu View PDF HTML (experimental) Abstract: For algebraic stacks over number fields, we define their Brauer-Manin sets, Brauer-Manin pairings, and extend the descent theory of Colliot-Thélène and Sansuc. By extending Sansuc's exact sequence, we show the torsionness of Brauer groups of stacks that are locally quotients of varieties by linear groups. With mild assumptions, for stacks that are locally quotients or Deligne-Mumford, we show that the Brauer-Manin obstruction coincides with some other cohomological obstructions such as obstructions given by torsors under connected groups or abelian gerbes. For Brauer-Manin sets of these stacks, we show the properties such as descent along a torsor, product preservation are still correct. These results extend classical theories of those on varieties. Comments: 25 pages, supplements additional citations and proofs, such as cohomological descent, representability of contracted products, and other general revisions. (git commit a496eec) Subjects: Algebraic Geometry (math.AG) ; Number Theory (math.NT) MSC classes: Primary 14G12, secondary 14A20, 14F22, 14F20 Cite as: arXiv:2306.14426 [math.AG] (or arXiv:2306.14426v3 [math.AG] for this version) https://doi.org/10.48550/arXiv.2306.14426 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Chang Lv [ view email ] [v1] Mon, 26 Jun 2023 05:36:47 UTC (21 KB) [v2] Sun, 30 Jul 2023 09:24:14 UTC (22 KB) [v3] Thu, 30 Apr 2026 03:30:27 UTC (33 KB) Full-text links: Access Paper: View a PDF of the paper titled The Brauer-Manin obstruction on algebraic stacks, by Chang Lv and Han Wu View PDF HTML (experimental) TeX Source view license Current browse context: math.AG < prev | next > new | recent | 2023-06 Change to browse by: math math.NT References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: 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