Automorphisms of finite fields from isogeny cycles

[2603.19428] Automorphisms of finite fields from isogeny cycles Skip to main content Search Submit Donate Log in Mathematics > Number Theory arXiv:2603.19428 (math) [Submitted on 19 Mar 2026 ( v1 ), last revised 27 Aug 2026 (this version, v2)] Title: Automorphisms of finite fields from isogeny cycles Authors: Kéva Djambaé View PDF HTML (experimental) Abstract: We develop an explicit geometric construction of automorphisms of finite fields arising from isogeny cycles. Let $k$ be a finite field, $E/k$ an elliptic curve, and $\ell$ an integer coprime to $\mathrm{char}(k)$. Let $\mathfrak{h}$ be an ideal of $\mathrm{End}(E)$ dividing $\ell$, and consider the corresponding torsion subgroup $E[\mathfrak{h}]\subseteq E[\ell]$. From the action of End(E) on $E[\mathfrak{h}]$, we construct the splitting field $K$ of the $x$-coordinates of points in $E[\mathfrak{h}]$ and the associated Galois group $\mathrm{Gal}(K/k)$. This yields $(\mathrm{End}(E)/\mathfrak{h})^* \to \mathrm{Gal}(K/k)$ a group homomorphism. Subjects: Number Theory (math.NT) ; Algebraic Geometry (math.AG) Cite as: arXiv:2603.19428 [math.NT] (or arXiv:2603.19428v2 [math.NT] for this version) https://doi.org/10.48550/arXiv.2603.19428 Focus to learn more arXiv-issued DOI via DataCite Related DOI : https://doi.org/10.1016/j.ffa.2026.102922 Focus to learn more DOI(s) linking to related resources Submission history From: Kéva Djambaé [ view email ] [v1] Thu, 19 Mar 2026 19:42:59 UTC (17 KB) [v2] Thu, 27 Aug 2026 02:34:14 UTC (19 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.NT < prev | next > new | recent | 2026-03 Change to browse by: math math.AG 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)

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