4 problems

Let $E$ be a coefficient field embeddable into $\mathbb C$, let $R$ be a finitely reduced Noetherian $E$-algebra, let $\Sigma$ be a fixed Zariski-dense subset of closed points of…

Let $E/F$ be a quadratic extension of local fields, let $v$ be a place of $F$, and let $G=U(W)\times U(V)$ and $G'$ be the corresponding local groups. Let…

Let $F$ be a number field, let $E/F$ be a quadratic extension, and let $v$ be a place of $F$. Let $G$ and $G'$ be the local groups in Zhang's comparison of relative trace formulas,…

Let $\pi$ be a tempered cuspidal automorphic representation of $G(\mathbb A)$, and let $J_\pi$ and $J^{\natural}_{\pi_v}$ denote the global and normalized local spherical character…