[2110.15035] Varieties with ample Frobenius-trace kernel Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Algebraic Geometry arXiv:2110.15035 (math) [Submitted on 28 Oct 2021 ( v1 ), last revised 2 Jun 2025 (this version, v3)] Title: Varieties with ample Frobenius-trace kernel Authors: Javier Carvajal-Rojas , Zsolt Patakfalvi View a PDF of the paper titled Varieties with ample Frobenius-trace kernel, by Javier Carvajal-Rojas and Zsolt Patakfalvi View PDF HTML (experimental) Abstract: In the search of a projective analog of Kunz's theorem and a Frobenius-theoretic analog of Mori--Hartshorne's theorem, we investigate the positivity of the kernel of the Frobenius trace (equivalently, the negativity of the cokernel of the Frobenius endomorphism) on a smooth projective variety over an algebraically closed field of positive characteristic. For instance, such kernel is ample for projective spaces. Conversely, we show that for curves, surfaces, and threefolds the Frobenius trace kernel is ample only for Fano varieties of Picard rank $1$. Comments: 41 pages, last version, accepted for publication in Annales Henri Lebesgue Subjects: Algebraic Geometry (math.AG) ; Commutative Algebra (math.AC) MSC classes: 14G17, 14J45, 14E30, 14J30, 14J26 Cite as: arXiv:2110.15035 [math.AG] (or arXiv:2110.15035v3 [math.AG] for this version) https://doi.org/10.48550/arXiv.2110.15035 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Annales Henri Lebesgue, Volume 8 (2025), pp. 721-767 Related DOI : https://doi.org/10.5802/ahl.247 Focus to learn more DOI(s) linking to related resources Submission history From: Javier Carvajal-Rojas [ view email ] [v1] Thu, 28 Oct 2021 11:47:07 UTC (54 KB) [v2] Thu, 18 May 2023 16:32:37 UTC (56 KB) [v3] Mon, 2 Jun 2025 14:17:09 UTC (49 KB) Full-text links: Access Paper: View a PDF of the paper titled Varieties with ample Frobenius-trace kernel, by Javier Carvajal-Rojas and Zsolt Patakfalvi View PDF HTML (experimental) TeX Source view license Current browse context: math.AG < prev | next > new | recent | 2021-10 Change to browse by: math math.AC 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