7 problems

Let $\mathcal{C}$ be the family locus under consideration, let $\kappa_{{\mathbf{g}},{\mathbf h}}\vert_{\mathcal{C}}$ be the restriction of the Beilinson–Flach cohomology class, an…

Let $L_p^{(c)}(\pi,s)=\mathscr{L}_p^{(c)}(\pi,\langle-\rangle^s)$ for $s\in\mathbb{Z}_p$, where $\langle-\rangle:\mathbb{Z}_p^{\times}\to1+2p\mathbb{Z}_p$ is the natural map. Let…

Let $k_{\Gamma}/k$ be a $\mathbb{Z}_p$-extension with Galois group $\Gamma$, let $\Gamma_n:=\operatorname{Gal}(k_n/k)$, and put $L_\Gamma:=k_\Gamma L$. Let…

Let $f$ be a newform of even weight $k\geq 2$ for $\Gamma_0(pN)$, where $p$ is prime and $p\nmid N$, and let $\chi$ be a Dirichlet character of conductor prime to $pN$ with…

Let $\mathbf{f}$ be the Hilbert modular form in the paper, let $F$ be its totally real coefficient field, and let $m$ be the parameter for which the trivial zero occurs at $s=m+1$.…

Let $G(T,V)$ and $\mathcal{E}(V)$ be as above, and let $g$ be the number of vanishing factors of $\mathcal{E}(V)$. Let $\mathcal{E}^*(V)$ denote the product of the nonzero factors,…

Let $M$ be a $p$-ordinary motive, let $L_p(s,M,\chi)$ be its analytic $p$-adic $L$-function, and let $a_0$ be a critical integer with character $\chi_0$ such that the interpolation…