5 problems

Let $F$ be a totally real number field, let $r$ be a positive integer, and let $A$ be an elliptic curve over $F$ with no complex multiplication over $\ovl F$. Suppose there exist a…

Global Gross–Prasad conjecture. The period is non-zero if and only if

Let $F$ be a number field, let $v$ be a place of $F$, let $\Pi_v$ be an irreducible smooth representation of $G(F_v)$, and let $\Sigma_v=\Sigma_{1,v}\boxtimes\Sigma_{2,v}$ be an ir…

Liu's refined global Gross–Prasad conjecture. One has

Let $V_{m+1}$ be an orthogonal space of dimension $m+1$, and let $V_m$ be a non-degenerate codimension-one subspace. Assume that…