Comparing local-global obstructions on algebraic stacks

[2608.02141] Comparing local-global obstructions on algebraic stacks Skip to main content Search Submit Donate Log in Mathematics > Algebraic Geometry arXiv:2608.02141 (math) [Submitted on 3 Aug 2026 ( v1 ), last revised 28 Aug 2026 (this version, v2)] Title: Comparing local-global obstructions on algebraic stacks Authors: Chang Lv , Han Wu , Xucheng Zhang View PDF HTML (experimental) Abstract: Let k be a number field. For quotient stacks [X/G] with X a smooth quasi-projective geometrically integral k-variety and G a linear k-group, we extend several relations between local-global obstructions previously known for varieties, showing that étale-Brauer obstruction is the finest among various obstructions (such as iterated descent, finite descent, descent, Brauer-Manin). Comments: Section 3 was rewritten with new lemmas fixing geometric-integrality plus typo/layout polish. 18 pages, git commit 81c812 Subjects: Algebraic Geometry (math.AG) ; Number Theory (math.NT) MSC classes: 14G05(primary), 14G12, 14A20, 14L30 (secondary) Cite as: arXiv:2608.02141 [math.AG] (or arXiv:2608.02141v2 [math.AG] for this version) https://doi.org/10.48550/arXiv.2608.02141 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Chang Lv [ view email ] [v1] Mon, 3 Aug 2026 12:28:30 UTC (22 KB) [v2] Fri, 28 Aug 2026 05:22:56 UTC (25 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.AG < prev | next > new | recent | 2026-08 Change to browse by: math math.NT 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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