6 problems

Let $F/F_0$ be an unramified quadratic extension of $p$-adic fields for an odd prime $p$. Let $S_n$ be the Jacquet–Rallis symmetric space, let $G_i=\mathrm{U}(V_i^\sharp)$ and…

Guo–Jacquet fundamental lemma. One has

Arithmetic fundamental lemma. For every regular semisimple orbit $(\zeta,y)$ in the minus set,

Relative fundamental lemma. For every regular semisimple orbit $(\zeta,y)$, the normalized orbital integral with the characteristic functions of $\mathrm{S}_n(O_F)$ and…

Let $F$ be the base local field, let $K/K_3$ be unramified, and let … be embeddings such that $(\Phi_1,\Phi_2)$ is a regular semisimple pair and $(\Phi_0,\Phi_3)$ is regular semisi…

Let $F$ be the base local field, let $K_0,K_1,K_2,K_3$ be the quadratic $F$-algebras arising from a biquadratic extension, and let … be $F$-algebra embeddings. Assume that…