8 problems

Let $U$ be the affinoid neighbourhood of a finite-slope classical point $x_0$ on the Rankin–Selberg eigenvariety, with $U$ smooth, the weight map finite étale, and classical cuspid…

Let $A_j$ be the Galois representation in the Rankin–Selberg setting, let $K_\infty$ be the relevant cyclotomic extension, and let $\Lambda$ be its Iwasawa algebra. Let…

Let $\Pi_0$ and $\Pi_1$ be relevant representations of $\operatorname{GL}_{n_0}(\mathbb{A}_F)$ and $\operatorname{GL}_{n_1}(\mathbb{A}_F)$, respectively, and let…

The Fitting-ideal conjecture. If $e_\eta\cdot L_p\neq 0$, then $e_\eta\cdot\mathcal{S}$ is a torsion $e_\eta\cdot\mathcal{O}(X)$-module, and

Let $\mathcal{S}=\\{(\triangle,\square),(\bullet,\circ)\\}$ be a quadruply-signed pair, let $\Gamma_{\mathrm{tor}}$ and $\Gamma_1$ be the torsion and pro-$p$ components of the cycl…

Let $f$) and $g$ be the two non-ordinary eigenforms, and let the four newly constructed $p$-adic $L$-functions be those associated with the four choices $(\beta_f,\beta_g)$,…

Let $\Pi$ and $\Pi'$ be the cohomological automorphic representations considered in the paper, of respective ranks $n$ and $n'$, with associated motives $M(\Pi)$ and $M(\Pi')$. Let…

Let $\varphi(z)$ be a normalized holomorphic Hecke eigenform of weight $\kappa$ for $SL_2(\mathbb{Z})$, with Fourier coefficients $a(n)$, and define … For the Rankin–Selberg error…