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Results tagged with local-fields
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user 52824
5
votes
Accepted
Why is the norm map dual to restriction under Tate local duality?
Note first of all that the "norm" map you speak of does not make sense unless the field extension is separable. That is, for a separable field extension $k'/k$ of finite degree and a commutative $k$- …
- 1,285
1
vote
Compact elements in $G(K)$ for a reductive group $G$ over a nonarchimedean local field $K$
It should be that $G(K)^0$ is the group of $g \in G(K)$ such that $|\chi(g)| = 1$ for all $K$-rational characters $\chi:G \rightarrow {\rm{GL}}_1$.
Once this is shown, it follows that $G(K)/G(K)^0$ …
6
votes
Accepted
Theorem 7b of Serre's "Propriétés galoisiennes des points d'ordre fini des courbes elliptiques"
This is ultimately an application of Lang's vanishing theorem for degree-1 Galois cohomology of connected algebraic groups over finite fields (applied to tori).
What follows may look complicated if y …