A formalization of Dedekind domains and class groups of global fields

@inproceedings{Baanen2021AFO,
  title={A formalization of Dedekind domains and class groups of global fields},
  author={Anne Baanen and Sander R. Dahmen and Ashvni Narayanan and Filippo Alberto Edoardo Nuccio},
  booktitle={ITP},
  year={2021}
}
Dedekind domains and their class groups are notions in commutative algebra that are essential in algebraic number theory. We formalized these structures and several fundamental properties, including number theoretic finiteness results for class groups, in the Lean prover as part of the mathlib mathematical library. This paper describes the formalization process, noting the idioms we found useful in our development and mathlib’s decentralized collaboration processes involved in this project. 
Formalizing Galois Theory
TLDR
A project to formalize Galois theory using the Lean theorem prover, which is part of a larger effort to formalized all of the standard undergraduate mathematics curriculum in Lean, formalizes the primitive element theorem, the fundamental theorem ofGalois theory, and the equivalence of several characterizations of finite degree Galois extensions. Expand
Scalar actions in Lean's mathlib
TLDR
This paper explores how Lean 3’s typeclasses are used by mathlib for scalar actions with examples, and illustrates some of the problems which come up when using them such as compatibility of actions and nondefinitionally-equal diamonds. Expand

References

SHOWING 1-10 OF 55 REFERENCES
Nine Chapters of Analytic Number Theory in Isabelle/HOL
TLDR
A formalisation of a large portion of Apostol’s Introduction to Analytic Number Theory in Isabelle/HOL is presented, including results on the Riemann and Hurwitz ζ functions and the Dirichlet L functions. Expand
Minkowski’s theorem. Archive of Formal Proofs (2017). https://isa-afp.org/entries/Minkowskis Theorem.html, Formal proof development
  • 2017
Metamath: A Computer Language for Mathematical Proofs
  • 2019
The Mathematical Components Libraries
  • Zenodo, Genève, Switzerland (2017)
  • 2017
A Uniform Proof of the Finiteness of the Class Group of a Global Field
TLDR
A definition of a class of Dedekind domains which includes the rings of integers of global fields and a proof that all rings in this class have finite ideal class group is given. Expand
Capriglio, F.A.E.: A Formalization of Dedekind Domains and Class Groups of Global Fields
  • ITP 2021. LIPIcs,
  • 2021
Gaussian integers. Archive of Formal Proofs
  • 2020
Gaussian integers. Archive of Formal Proofs (2020). https:// isa-afp.org/entries/Gaussian Integers.html, Formal proof development
  • 2020
Gaussian integers. Archive of Formal Proofs, 2020
  • 2020
Gaussian integers. Archive of Formal Proofs, April 2020. https://isa-afp.org/ entries/Gaussian_Integers.html, Formal proof development
  • 2020
...
1
2
3
4
5
...