The Lichtenbaum-Quillen dimension of complex varieties

[2312.06930] The Lichtenbaum-Quillen dimension of complex varieties Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Algebraic Geometry arXiv:2312.06930 (math) [Submitted on 12 Dec 2023 ( v1 ), last revised 4 Aug 2026 (this version, v4)] Title: The Lichtenbaum-Quillen dimension of complex varieties Authors: Nicolas Addington , Elden Elmanto View a PDF of the paper titled The Lichtenbaum-Quillen dimension of complex varieties, by Nicolas Addington and Elden Elmanto View PDF HTML (experimental) Abstract: The Lichtenbaum-Quillen conjecture for smooth complex varieties states that algebraic and topological K-theory with finite coefficients become isomorphic in high degrees. We define the "Lichtenbaum-Quillen dimension" of a variety in terms of the point where this happens, show that it is surprisingly computable, and analyze many examples. It gives an obstruction to rationality, but one that turns out to be weaker than unramified cohomology and some related birational invariants defined by Colliot-Thélène and Voisin using Bloch-Ogus theory. Because it is compatible with semi-orthogonal decompositions, however, it allows us to prove some new cases of the integral Hodge conjecture using homological projective duality, and to compute the higher algebraic K-theory of the Kuznetsov components of the derived categories of some Fano varieties. Comments: 60 pages. v4: further improvements following referee's suggestions Subjects: Algebraic Geometry (math.AG) ; Algebraic Topology (math.AT); K-Theory and Homology (math.KT) Cite as: arXiv:2312.06930 [math.AG] (or arXiv:2312.06930v4 [math.AG] for this version) https://doi.org/10.48550/arXiv.2312.06930 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Nicolas Addington [ view email ] [v1] Tue, 12 Dec 2023 01:59:55 UTC (39 KB) [v2] Fri, 26 Apr 2024 18:14:22 UTC (41 KB) [v3] Fri, 10 Apr 2026 22:22:46 UTC (42 KB) [v4] Tue, 4 Aug 2026 12:43:35 UTC (43 KB) Full-text links: Access Paper: View a PDF of the paper titled The Lichtenbaum-Quillen dimension of complex varieties, by Nicolas Addington and Elden Elmanto View PDF HTML (experimental) TeX Source view license Current browse context: math.AG < prev | next > new | recent | 2023-12 Change to browse by: math math.AT math.KT 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

Related documents

• Gorenstein dimensions and Hirsch length of groups#986910
• Matijevic-Roberts type theorems, Rees rings and associated graded rings#365120
• Completed cohomology of Hilbert modular varieties below middle degree#1063521
• Bounds for Codimension-One Components of Zero Loci of Bernstein-Sato Ideals#1014916
• Relative Global Dimension of Controllable Extensions#1115598