2 problems

Let $\chi = \chi_0 \chi_p$, with $\chi_0 \ne 1$, be an even irreducible rational character and let $K=K_\chi$. For every irreducible $p$-adic character $\varphi$ dividing $\chi$, s…

For each integer $s\geq 0$, let ${\rm ES}_{s}(T)$ denote the module of Euler systems of rank $s$ for a representation $T$. An Euler system is called basic when it has the distingui…