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Formalising perfectoid spaces

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Title: Formalising perfectoid spaces
Authors: Buzzard, K
Commelin, J
Massot, P
Item Type: Conference Paper
Abstract: Perfectoid spaces are sophisticated objects in arithmetic geometry introduced by Peter Scholze in 2012. We formalised enough definitions and theorems in topology, algebra and geometry to define perfectoid spaces in the Lean theorem prover. This experiment confirms that a proof assistant can handle complexity in that direction, which is rather different from formalising a long proof about simple objects. It also confirms that mathematicians with no computer science training can become proficient users of a proof assistant in a relatively short period of time. Finally, we observe that formalising a piece of mathematics that is a trending topic boosts the visibility of proof assistants amongst pure mathematicians.
Issue Date: 1-Jan-2020
Date of Acceptance: 1-Jan-2020
URI: http://hdl.handle.net/10044/1/76749
DOI: 10.1145/3372885.3373830
ISBN: 978-1-4503-7097-4
Publisher: Association for Computing Machinery
Start Page: 299
End Page: 312
Journal / Book Title: Proceedings of the 9th ACM SIGPLAN International Conference on Certified Programs and Proofs
Copyright Statement: © 2019 The Author(s)
Conference Name: POPL: Principles of Programming Languages
Keywords: cs.LO
Notes: 19 pages, see also https://leanprover-community.github.io/lean-perfectoid-spaces/
Publication Status: Published
Conference Place: New Orleans, USA
Open Access location: https://dl.acm.org/doi/10.1145/3372885.3373830
Online Publication Date: 2020-01-01
Appears in Collections:Pure Mathematics
Faculty of Natural Sciences