6 problems

The existence conjecture for $p$-adic Asai $L$-functions. There exists an element

Let $\mathcal{M}=\mathcal{M}(\pi,r^{\pm}\otimes\Psi)$ be critical, with Betti and de Rham realizations $H_{\rm B}(\mathcal{M})$ and $H_{\rm dR}(\mathcal{M})$, and let…

Asai $p$-adic $L$-function conjecture. Both $L_{\mathfrak{p},\mathrm{Asai}}(\mathcal{F})$ and $L_{\mathfrak{p},\mathrm{Asai}}^{\operatorname{imp}}(\mathcal{F})$ should be analytic…

Let $K/\mathbf{Q}$ be the quadratic extension, let $\pi$ be the automorphic representation and let $q>2k$ be a prime at which neither $\pi$ nor $K/\mathbf{Q}$ is ramified. Let…

Let $Fsubset K$ be a quadratic extension of local fields, let $G_n(K)=GL(n,K)$, and let $W'_K$ and $W'_F$ be the Weil–Deligne groups. For a finite-dimensional representation $\rho$…

Jacquet's conjecture. For representations $c0$ whose central character is trivial on $F^*$, the condition