7 problems

Let $F$ be a number field, $E$ a number field, $M$ a polarized motive in the pseudo-Abelian category of Chow motives over $F$ with coefficients in $E$, and let $\lbd$ be a finite p…

Let $f\in S_k(\Gamma_0(N))$ be a newform, let $p\ge 3$ be a prime, and suppose that $\rho_f$ has large image. Let $\widetilde{\boldsymbol{\delta}}^{\mathrm{min},\dagger}$ denote th…

Let $E$ be the number field in the paper, let $\rho\colon G_E\to \operatorname{GL}_n(\overline{\mathbf{Q}}{}_p)$ be an irreducible geometric representation of weight $-1$, and let…

Let $K$ be a number field. Define the analytic rank of the modular motive by … and let r_\mathrm{alg}(\mathcal{M}/K)=\dim_F H^1_\operatorname{mot}(K,\mathcal{M}) be the algebraic…

Let $(\Pi,\underline{\mathcal G})$ satisfy the stated Galois-representation, ordinarity, residual non-Eisenstein, and $p$-distinguished hypotheses. For a classical specialisation…

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…

Let $f$ be a modular form of even weight $r+2$, let $\psi$ be an unramified algebraic Hecke character of an imaginary quadratic field $K$ of infinity type $(r,0)$, and let $W$ be t…