On the locus of $2$-dimensional crystalline representations with a given reduction modulo $p$

Sandra Rozensztajn

We consider the family of irreducible crystalline representations of dimension $2$ of $\mathrm{Gal}({\overline{\mathbf{Q}}}_p/{\mathbf{Q}}_p)$ given by the $V_{k,a_p}$ for a fixed weight integer…