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Results tagged with absolute-galois-group
Search options questions only
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user 102216
3
votes
1
answer
225
views
induced isomorphism in continuous cohomology
Suppose that we have a morphism between profinite groups $f: G_{1}\rightarrow G_{2}$ such that $f^{\ast}:H_{cont}^{\ast}(G_{2},A)\rightarrow H_{cont}^{\ast}(G_{1},A) $ is an isomorphism for any finite …
- 771
16
votes
1
answer
1k
views
What "should" be the absolute galois group of a field with one element
As far as I know there is many "suggestions" of what should be a "field with one element" $\mathbf{F}_{1}$.
My question is the following:
How we should think or what should be the "absolute Galois …
- 771
31
votes
3
answers
1k
views
Consequences of Shafarevich conjecture
The Shafarevich conjecture states that the Galois group $\mathrm{Gal}({\overline{\mathbf{Q}}/\mathbf{Q}^{ab}})$ is a free profinite group, where $\mathbf{Q}^{ab}$ is the maximal abelian extension of $ …
- 771