AbsoluteGaloisGroup.lean`

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2 declarations, 0 contain sorry, 0 declared as axioms

Restriction maps of absolute Galois groups

These definitions were introduced in Mathlib by Thomas Browning's pull request #41415. They are absent from this repository's Mathlib v4.33.1 dependency. The added code is copied verbatim from Mathlib.FieldTheory.AbsoluteGaloisGroup at the merged commit 7e604dbff1442ed4b05a0b9a4b15c5207584f116.

Imports (1)

Mathlib.FieldTheory.AbsoluteGaloisGroup

Imported by 2 files

def Field.absoluteGaloisGroup.mapOfAlgebra A commuting square of two fields and their algebraic closures induces a continuous homomorphism of their absolute Galois groups line 53 source
Source documentation
A commuting square of two fields and their algebraic closures induces a continuous homomorphism of their absolute Galois groups.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Field, Algebra, AlgebraicClosure, IsScalarTower, ContinuousMonoidHom, Field.absoluteGaloisGroup
Proof uses: MonoidHom, MonoidHom.comp, AlgEquiv, AlgEquiv.restrictNormalHom, AlgEquiv.restrictScalarsHom, ContinuousMonoidHom.mk
67 instances, coercions and auxiliary constants left out.

Tactic trace: 17 steps
Open to load the checked before-and-after goal states.
```
noncomputable def absoluteGaloisGroup.mapOfAlgebra : G_K L →ₜ* G_K K :=
…
```
def Field.absoluteGaloisGroup.map An embedding of fields induces a continuous homomorphism of absolute Galois groups line 81 source
Source documentation
An embedding of fields induces a continuous homomorphism of absolute Galois groups. Note that this depends on an arbitrary choice of embedding of the algebraic closures.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Field, RingHom, ContinuousMonoidHom, Field.absoluteGaloisGroup
Proof uses: Field.absoluteGaloisGroup.mapOfAlgebra, RingHom.toAlgebra, AlgebraicClosure, AlgHom.toRingHom, IsAlgClosed.lift
25 instances, coercions and auxiliary constants left out.
```
noncomputable def absoluteGaloisGroup.map (f : K →+* L) : G_K L →ₜ* G_K K :=
…
```