Etale cohomology of diamonds

[1709.07343] Etale cohomology of diamonds Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Algebraic Geometry arXiv:1709.07343 (math) [Submitted on 21 Sep 2017 ( v1 ), last revised 14 Apr 2026 (this version, v4)] Title: Etale cohomology of diamonds Authors: Peter Scholze View a PDF of the paper titled Etale cohomology of diamonds, by Peter Scholze View PDF HTML (experimental) Abstract: Motivated by problems on the étale cohomology of Rapoport--Zink spaces and their generalizations, as well as Fargues's geometrization conjecture for the local Langlands correspondence, we develop a six functor formalism for the étale cohomology of diamonds, and more generally small v-stacks on the category of perfectoid spaces of characteristic $p$. Using a natural functor from analytic adic spaces over $\mathbb Z_p$ to diamonds which identifies étale sites, this induces a similar formalism in that setting, which in the noetherian setting recovers the formalism from Huber's book. Comments: 168 pages, final version to appear in Asterisque Subjects: Algebraic Geometry (math.AG) ; Number Theory (math.NT) MSC classes: 14F20, 14F05, 14G22, 14G20 Cite as: arXiv:1709.07343 [math.AG] (or arXiv:1709.07343v4 [math.AG] for this version) https://doi.org/10.48550/arXiv.1709.07343 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Peter Scholze [ view email ] [v1] Thu, 21 Sep 2017 14:27:30 UTC (133 KB) [v2] Fri, 26 Feb 2021 13:21:49 UTC (143 KB) [v3] Thu, 27 Jan 2022 07:39:54 UTC (145 KB) [v4] Tue, 14 Apr 2026 07:29:30 UTC (151 KB) Full-text links: Access Paper: View a PDF of the paper titled Etale cohomology of diamonds, by Peter Scholze View PDF HTML (experimental) TeX Source view license Current browse context: math.AG < prev | next > new | recent | 2017-09 Change to browse by: math math.NT References & Citations NASA ADS Google Scholar Semantic Scholar 2 blog links ( what is this? ) 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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