{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/etale-cohomology-of-diamonds","title":"Etale cohomology of diamonds","arxiv_id":"1709.07343","date":"2017-09-21","proceeding":null,"authors":["Peter Scholze"],"abstract":"Motivated by problems on the \\'etale 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 \\'etale 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 \\'etale sites, this induces a similar formalism in that setting, which in the noetherian setting recovers the formalism from Huber's book.","url_abs":"https://arxiv.org/abs/1709.07343v3","url_pdf":"https://arxiv.org/pdf/1709.07343v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"etale-cohomology-of-diamonds","repo_url":"https://github.com/kbuzzard/lean-perfectoid-spaces","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"etale-cohomology-of-diamonds","repo_url":"https://github.com/leanprover-community/lean-perfectoid-spaces","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}