[2304.02415] Utilisation de l'aplatissement en géométrie de Berkovich Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Algebraic Geometry arXiv:2304.02415 (math) [Submitted on 5 Apr 2023 ( v1 ), last revised 28 Apr 2026 (this version, v3)] Title: Utilisation de l'aplatissement en géométrie de Berkovich Authors: Antoine Ducros View a PDF of the paper titled Utilisation de l'aplatissement en g\'eom\'etrie de Berkovich, by Antoine Ducros View PDF HTML (experimental) Abstract: In this article, we carry out the flattening techniques developped in a former work in order to ``embellish" a map between compact analytic spaces, to describe the structure of its image, getting this way a substitute for Chevalley's theorem in the non-archimedean setting, and finally to show that flatness in the world of Berkovich spaces amounts to naive flatness provided one works with local rings for the G-topology Comments: 51 pages, French; this is the final version, to appear in Annales de l'institut Fourier Subjects: Algebraic Geometry (math.AG) MSC classes: 14G22, 14G99 Cite as: arXiv:2304.02415 [math.AG] (or arXiv:2304.02415v3 [math.AG] for this version) https://doi.org/10.48550/arXiv.2304.02415 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Antoine Ducros [ view email ] [v1] Wed, 5 Apr 2023 12:54:45 UTC (67 KB) [v2] Fri, 28 Apr 2023 11:14:14 UTC (67 KB) [v3] Tue, 28 Apr 2026 09:26:23 UTC (97 KB) Full-text links: Access Paper: View a PDF of the paper titled Utilisation de l'aplatissement en g\'eom\'etrie de Berkovich, by Antoine Ducros View PDF HTML (experimental) TeX Source view license Current browse context: math.AG < prev | next > new | recent | 2023-04 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