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Results tagged with local-fields
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user 4351
3
votes
Accepted
What are the open normal subgroups of the inertia group of a local field?
As all the responses indicate, the answer to my question is "yes." The most direct route seems to be the one suggested by KConrad. Explicitly, if $F/K_{un}$ is Galois of degree $e$ (inside $K_s$), the …
- 3,380
7
votes
What's the minimum number of generators for the wild inertia?
You have the inflation restriction sequence $0\rightarrow H^1(K^{nr}/K,\mathbf{F}_p)\rightarrow H^1(K,\mathbf{F}_p)\rightarrow H^1(K^{nr},\mathbf{F}_p)^{\mathrm{Gal}(K^{nr}/K)}\rightarrow 0$ with the …
- 3,380
3
votes
2
answers
1k
views
What are the open normal subgroups of the inertia group of a local field?
Let $K$ be a non-Archimedean local field, i.e., complete with respect to a non-trivial, non-archimedean discrete absolute value, with finite residue field $k$ of characteristic $p\neq 0$. Also let $K_ …
- 3,380
3
votes
Accepted
Weil group of a local field, small notational problem
If $G$ is any profinite group, and $a\in\widehat{\mathbf{Z}}$, then for any sequence $(a_n)$ of integers converging in $\widehat{\mathbf{Z}}$ to $a$, the sequence $(g^{a_n})$ converges in $g$ to an el …
- 3,380