Reductions of certain 3-dimensional crystalline representations

Abstract

We compute reduction $\bar{\rho }$ of 3-dimensional irreducible crystalline representations $\rho$ of $G_{{\mathbb{Q}}_p}$ with Hodge-Tate weights $\{0,r,s\}$ satisfying $2\le r\le p-2,2+p\le s\le r+p-2.$ If $\bar{\rho }$ is irreducible then we show that the generic fiber of crystalline universal deformation ring of $\bar{\rho }$ is connected.

23 pages

References in corpus (1)

• Reductions of $2$-dimensional semi-stable representations with large $\mathcal{L}$-invariant

Cited by in corpus (1)

• On the existence of analytic families of G-stable lattices and their reductions