3 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 $X$ be a compact Kähler manifold and let $C\subset X$ be a smooth curve with ample normal bundle. Write $[C]$ for its cohomology class and let $\mathcal{K}(X)$ denote the Kähle…

Let $f$ be a cusp form with algebraic coefficients, and let $E(f)$ denote its Klingen Eisenstein series. Garrett's conjecture. The Klingen Eisenstein series $E(f)$ has algebraic co…