4 problems

Let $\pi$ be an automorphic representation of $\operatorname{GL}_n(\mathbb{A})$, and define its field of rationality by … Call $\pi$ algebraic in Clozel’s sense. Clozel's algebraic…

Let $G/F$ be a connected reductive group, and let $|W|$ be the cardinality of the Weyl group of a maximal torus in $G\times\overline{F}$. Let $\mathfrak{p}$ be a prime such that…

Let $F$ be a number field, let $G$ be a connected reductive group over $F$, let $S$ be a finite set of places containing the ramified finite places of $G$ and all infinite places,…

Let $G$ be a connected reductive group over $\mathbb{Q}$ and let $\pi$ be an automorphic representation of $G(\mathbb{A})$. The field of rationality $\mathbb{Q}(\pi)$ is the field…