Theorems · Definition · number theory
ValuationSubring.decompositionSubgroup
(K : Type u_1) →
{L : Type u_2} →
[inst : Field K] → [inst_1 : Field L] → [inst_2 : Algebra K L] → ValuationSubring L → Subgroup Gal(L/K)The decomposition subgroup defined as the stabilizer of the action on the type of all valuation subrings of the field.
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 56 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
- Subgroupstatement · cited by 3,593
- AlgEquivstatement and proof · cited by 1,681
- MulAction.stabilizerproof · cited by 254
- ValuationSubringstatement and proof · cited by 187
Cited by2
Results whose statement or proof uses this declaration.
- ValuationSubring.inertiaSubgroupstatement and proof · cited by 0
- ValuationSubring.subMulActionstatement · cited by 0