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[Merged by Bors] - feat(NumberField/CanonicalEmbedding/FundamentalCone): Prove equivalence with principal ideals #12333
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… the action of the units of a number field (#12268) Let `K` be a number field of signature `(r₁, r₂)`. This PR defines the fundamental cone: it is a cone in the mixed space that is a fundamental domain for the action of `(𝓞 K)ˣ` modulo torsion. In a later PR #12333, we prove that points in the fundamental cone coming from `(𝓞 K)` modulo torsion are in a norm-preserving correspondence with the non-zero principal ideals of `(𝓞 K)`. This PR is part of the proof of the Analytic Class Number Formula. Co-authored-by: Xavier Roblot <[email protected]>
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Thanks!
bors d+
Mathlib/NumberTheory/NumberField/CanonicalEmbedding/FundamentalCone.lean
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✌️ xroblot can now approve this pull request. To approve and merge a pull request, simply reply with |
…lCone.lean Co-authored-by: Riccardo Brasca <[email protected]>
…e_equiv' into xfr_fundamental_cone_equiv
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…ce with principal ideals (#12333) We prove that there is an equiv between the nonzero integral points in the fundamental cone and the nonzero integral ideals of `K` and that this equiv preserves norm. This PR is part of the proof of the Analytic Class Number Formula. Co-authored-by: Xavier Roblot <[email protected]>
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feat(NumberField/CanonicalEmbedding/FundamentalCone): Prove equivalence with principal ideals
[Merged by Bors] - feat(NumberField/CanonicalEmbedding/FundamentalCone): Prove equivalence with principal ideals
Sep 23, 2024
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We prove that there is an equiv between the nonzero integral points in the fundamental cone and the nonzero integral ideals of
K
and that this equiv preserves norm.This PR is part of the proof of the Analytic Class Number Formula.
Ideal.associatesEquivIsPrincipal
for generators that are non-zero-divisors #12780