the emerton-gee stack for $\mathrm{gl}_2$ is a stack of $(\varphi, \gamma)$-modules whose reduced part $\mathcal{x}_{2, \mathrm{red}}$ can be viewed as a moduli stack of mod $p$ representations of a $p$-adic galois group. we compute criteria for codimension one intersections of the irreducible components of $\mathcal{x}_{2, \mathrm{red}}$, and interpret them in sheaf-theoretic terms. we also give a cohomological criterion for the number of top-dimensional components in a codimension one intersection.

[pre-talk at 1:20pm]