Theorems · Definition · field theory
galGroupBasis
(K : Type u_1) → (L : Type u_2) → [inst : Field K] → [inst_1 : Field L] → [inst_2 : Algebra K L] → GroupFilterBasis Gal(L/K)
For a field extension L/K, galGroupBasis K L is the group filter basis on Gal(L/K)
whose sets are Gal(L/E) for finite subextensions E/K.
- Defined in
- Mathlib.FieldTheory.KrullTopology
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 147 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- AlgEquivstatement and proof · cited by 1,681
- FilterBasisproof · cited by 23
- GroupFilterBasisstatement · cited by 18
- galBasisproof · cited by 1
Cited by6
Results whose statement or proof uses this declaration.
- IntermediateField.fixingSubgroup_isOpenproof · cited by 5
- krullTopology_mem_nhds_one_iffproof · cited by 2
- InfiniteGalois.isOpen_iff_finiteproof · cited by 1
- cyclotomicCharacter.continuousproof · cited by 0
- InfiniteGalois.fixingSubgroup_fixedFieldproof · cited by 0
- krullTopology_t2proof · cited by 0