7 problems

Let $H$ be the number field occurring in the Artin representation $\rho$, let $\mathbb{Q}_\infty$ be the cyclotomic $\mathbb{Z}_p$-extension of $\mathbb{Q}$, and let…

Let $\rho=\operatorname{Ind}_{\operatorname{G}_L}^{\mathbb{Q}}\zeta$ be an odd two-dimensional dihedral Artin representation, with $L$ imaginary quadratic, and let $S(\rho)$ be the…

Minimalist conjecture for twists. For $100\%$ of elliptic curves $E/\mathbb Q$,

Parity conjecture for Artin twists.

Let $\mathcal{F}/\mathcal{K}$ be a finite Galois extension, let $A$ be an abelian variety over the global field $\mathcal{K}$, and let $A(\mathcal{F})_{\mathbb{C}}$ be the…

Let $E$) be an elliptic curve and let $\rho$ be an Artin representation, both defined over $\mathbb{Q}$. Define the twisted $L$-function by … where … $H_l^1(E)$ is the dual of the…

Let $A$ be an abelian variety over a number field $K$, let $F/K$ be a Galois extension, let $p$ be a prime, and let $\tau$ be a self-dual representation of…