Perfectoid overconvergent Siegel modular forms and the overconvergent Eichler--Shimura morphism

[2106.00094] Perfectoid overconvergent Siegel modular forms and the overconvergent Eichler--Shimura morphism Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Number Theory arXiv:2106.00094 (math) [Submitted on 31 May 2021 ( v1 ), last revised 9 Apr 2026 (this version, v3)] Title: Perfectoid overconvergent Siegel modular forms and the overconvergent Eichler--Shimura morphism Authors: Hansheng Diao , Giovanni Rosso , Ju-Feng Wu View a PDF of the paper titled Perfectoid overconvergent Siegel modular forms and the overconvergent Eichler--Shimura morphism, by Hansheng Diao and 2 other authors View PDF HTML (experimental) Abstract: The aim of this paper is twofold. We first present a construction of the overconvergent automorphic sheaves for Siegel modular forms by generalising the perfectoid method, originally introduced by Chojecki--Hansen--Johansson for automorphic forms on compact Shimura curves over $\mathbf{Q}$. The global sections of these automorphic sheaves are precisely the overconvergent Siegel modular forms. In particular, one can compare these automorphic sheaves with the ones constructed by Andreatta--Iovita--Pilloni. Secondly, we establish an (explicit) overconvergent Eichler--Shimura morphism for Siegel modular forms, generalising the result of Andreatta--Iovita--Stevens for the elliptic modular forms. Comments: In Research in the Mathematical Sciences Subjects: Number Theory (math.NT) Cite as: arXiv:2106.00094 [math.NT] (or arXiv:2106.00094v3 [math.NT] for this version) https://doi.org/10.48550/arXiv.2106.00094 Focus to learn more arXiv-issued DOI via DataCite Related DOI : https://doi.org/10.1007/s40687-026-00610-5 Focus to learn more DOI(s) linking to related resources Submission history From: Ju-Feng Wu [ view email ] [v1] Mon, 31 May 2021 20:35:56 UTC (100 KB) [v2] Tue, 21 Sep 2021 19:07:45 UTC (101 KB) [v3] Thu, 9 Apr 2026 10:34:44 UTC (100 KB) Full-text links: Access Paper: View a PDF of the paper titled Perfectoid overconvergent Siegel modular forms and the overconvergent Eichler--Shimura morphism, by Hansheng Diao and 2 other authors View PDF HTML (experimental) TeX Source view license Current browse context: math.NT < prev | next > new | recent | 2021-06 Change to browse by: math 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

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