Theorems · Definition · number theory
NumberField.InfinitePlace.mult
{K : Type u_1} → [inst : Field K] → NumberField.InfinitePlace K → ℕThe multiplicity of an infinite place, that is the number of distinct complex embeddings that
define it, see card_filter_mk_eq.
- Cited by
- 107 results in Mathlib
- Foundations
- Depth 140 from the axioms, rests on 3,712 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fieldstatement and proof · cited by 7,404
- NumberField.InfinitePlacestatement and proof · cited by 604
- NumberField.InfinitePlace.IsRealproof · cited by 301
Cited by117
Results whose statement or proof uses this declaration.
- NumberField.mixedEmbedding.normproof · cited by 46
- NumberField.InfinitePlace.IsUnramifiedproof · cited by 35
- NumberField.Units.logEmbeddingproof · cited by 25
- NumberField.mixedEmbedding.logMapproof · cited by 21
- NumberField.mixedEmbedding.convexBodySumFunproof · cited by 14
- NumberField.mixedEmbedding.fundamentalCone.expMap_singleproof · cited by 8
- NumberField.InfinitePlace.prod_eq_abs_normstatement and proof · cited by 8
- NumberField.mixedEmbedding.norm_eq_normproof · cited by 7
- NumberField.InfinitePlace.sum_mult_eqstatement and proof · cited by 7
- NumberField.InfinitePlace.mult_posstatement · cited by 6
- NumberField.mixedEmbedding.norm_smulproof · cited by 5
- NumberField.mixedEmbedding.fundamentalCone.completeFamilyproof · cited by 5