Theorems · Theorem · number theory
NumberField.Embeddings.card
∀ (K : Type u_1) [inst : Field K] (A : Type u_2) [inst_1 : Field A] [inst_2 : CharZero A] [inst_3 : NumberField K] [IsAlgClosed A], Fintype.card (K →+* A) = Module.finrank ℚ K
The number of embeddings of a number field is equal to its finrank.
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 161 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Equiv.symmproof · cited by 3,681
- Module.finrankstatement and proof · cited by 1,770
- Fintype.cardstatement · cited by 1,386
- CharZerostatement and proof · cited by 932
- NumberFieldstatement and proof · cited by 653
- IsAlgClosedstatement and proof · cited by 150
- Fintype.ofEquiv_cardproof · cited by 16
- AlgHom.cardproof · cited by 10
- RingHom.equivRatAlgHomproof · cited by 8
Cited by6
Results whose statement or proof uses this declaration.
- NumberField.InfinitePlace.card_add_two_mul_card_eq_rankproof · cited by 9
- NumberField.InfinitePlace.sum_mult_eqproof · cited by 7
- NumberField.mixedEmbedding.finrankproof · cited by 4
- NumberField.InfinitePlace.ComplexEmbedding.conjugate_signproof · cited by 1
- NumberField.house.exists_ne_zero_int_vec_house_leproof · cited by 0
- NumberField.house.basis_repr_norm_le_const_mul_houseproof · cited by 0