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Results tagged with galois-cohomology
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user 102216
6
votes
1
answer
440
views
The second Milnor $K$-theory of a field
Let $\mathbf{Q}^{\mathrm{ab}}$ be the maximal abelian extension of the field of rational numbers $\mathbf{Q}$. I'm interested in the following question:
Is it true that $K^{M}_{2}(\mathbf{Q}^{\mathrm …
- 771
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
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