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Results tagged with local-fields
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user 4149
3
votes
Accepted
When is $G(R)\rightarrow G^{\textrm{ad}}(R)$ surjective?
$\require{AMScd}
$In this answer, $k$ is a nonarchimedean local field.
Lemma 1.
Consider a short exact sequence of linear algebraic $k$-groups
$$ 1\to C\overset i\longrightarrow G\overset j\longright …
- 14.2k
6
votes
Accepted
Characters of simply connected semsimple algebraic groups over local fields
As I have written in a comment, the answer is YES (any abstract homomorphism into an abelian group is trivial) when $G$ is an isotropic, simply connected, simple algebraic group over a nonarchmedean l …
- 14.2k
3
votes
0
answers
94
views
Multiplication law in a division algebra of dimension 9 over a non-archimedean local field
Let $k$ be a non-archimedean local field, for example, a $p$-adic field (a finite extension of the filed ${\Bbb Q}_p$ of $p$-adic numbers).
It is well known that there is a canonical isomorphism
$${\r …
- 14.2k