All Questions

Let $G$ be a semisimple algebraic group over $\mathbb{Q}_p$. Then by definition $G$ admits no non-trivial algebraic characters, i.e. homomorphisms $G \to \mathbb{G}_m$. However, it is quite possible ...

Let $F$ be a $p$-adic field and let $X$ be a smooth integral variety over $F$ (I am chiefly interested in the case when $X$ is a connected reductive group over $F$). Let $U$ be a non-empty open subset ...

Let $F$ be a totally real number field, $E$ a totally imaginary quadratic extension over $E$, and $V$ an hermitian $n$-dimensional vector space over $F$. I assume $n=2m$ is even. Let $U$ be a unitary ...

Let $G$ be a connected simple group over a local field $k$. Let $I\subset G(\mathcal{O})$ denote an Iwahori subgroup of $G(k)$ with Lie algebra $\mathfrak{i}$. Let $P\supseteq I$ be any other ...

Let $F$ be a non archimedean local field and let $G$ be linear algebraic group over $F$. I do not have a lot of experience with linear algebraic group, but it seems very obvious that $G$ inherits the ...