5 problems

Algebraicity and Shimura reciprocity conjecture. If $r_\mathrm{alg}(A/E,\chi)\ge r$, then there exists an element $w_A^\chi\in\wedge^r A(E_\mathfrak{c})^\chi$ such that

Let $V_p(f)$ be the two-dimensional representation attached to a Bianchi modular form, assume that $V_p(f)|_{G_{F_{\mathfrak p}}}$ is semistable, and let $\mathfrak p$, $K$,…

Let $K/F$ be a quadratic extension embedded in a quaternion algebra $B$, let $\mathcal{O}$ be an order in $K$, let $H^{\mathcal{O}}$ be its ring class field, and let $P_\tau$ be th…

Let $\mathfrak{b}$ be an invertible $\mathcal{O}$-ideal that is $\mathfrak{f}$-integral, let $\mathfrak{n}$ be an invertible $\mathcal{O}$-ideal satisfying … and let…

Let $[(r,\tau)]\in(\mathbb{Z}/f\mathbb{Z}\times H^{\mathcal{O}}(\mathfrak{N}))/\sim_f$ with $\tau$ reduced, set $\mathcal{O}=\mathcal{O}_{\tau}$, $\mathfrak{f}=f\mathcal{O}$,…