{"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/formalising-the-krull-topology-in-lean","title":"Formalising the Krull Topology in Lean","arxiv_id":"2207.09486","date":"2022-07-19","proceeding":null,"authors":["Sebastian Monnet"],"abstract":"The Galois group of an infinite Galois extension has a natural topology, called the Krull topology, which has the important property of being profinite. It is impossible to talk about Galois representations, and hence the Langlands Program, without first defining the Krull topology. We explain our formalisation of this topology, and our proof that it is profinite, in the Lean 3 theorem prover.","url_abs":"https://arxiv.org/abs/2207.09486v2","url_pdf":"https://arxiv.org/pdf/2207.09486v2.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":"formalising-the-krull-topology-in-lean","repo_url":"https://github.com/leanprover-community/mathlib","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok","spdx":"Apache-2.0"}}],"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}