4 problems

Let $p$ be an odd prime, let $\mathcal{W}$ be the weight space for $\operatorname{GL}_2$, and let $\mathcal{X}$ be an eigencurve with weight map…

Coleman–Mazur halo conjecture. The part of the eigencurve over the boundary of weight space should be a disjoint union of countably infinitely many connected components, the weight…

Let $p$ be a rational prime, let $N$ be a positive integer prime to $p$, let $\mathcal{W}$ be the $p$-adic weight space for $\mathit{GL}_{2,\mathbb{Q}}$, and let $\mathcal{C}_N$ be…

Let $\mathcal{W}$ be weight space with coordinate $T$, let $r<1$, and let $\mathcal{W}^{\geq r}$ be the sub-annulus where $r\leq |T|<1$. Put … Here $\operatorname{wt}$ is the weigh…