4 problems

Let $\mathcal X$ be sufficiently small, let $W(f)$ be the global root number of the family, and let ${}^{\rm c}V_\mathcal X$ and ${}^{\rm c}V'_\mathcal X$ be the relevant critical…

Let $\tilde\pi$ be a non-critical cuspidal representation, let $x_{\tilde\pi}\in\cE_{\cU,h}^\bullet$ be the associated point, and let $\cW$ be the weight space. Write $\ell$ for th…

Hida's codimension conjecture. We have

Let $F$ be an imaginary quadratic field and let $p$ be a split prime. Suppose that $\rho:\operatorname{Gal}(\overline{F}/F)\to\operatorname{GL}_2(E)$ is continuous, irreducible, ne…