Deformations of Reducible Galois Representations to Hida-Families

Abstract

The global deformation theory of residually reducible Galois representations with fixed auxiliary conditions is studied. We show that $\bar{\rho }:\mathrm{Gal}(\bar{\mathbb{Q}}/\mathbb{Q})\to {\mathrm{GL}}_2({\bar{\mathbb{F}}}_p)$ lifts to a Hida line for which the weights range over a congruence class modulo-$p^2$. The advantage of the purely Galois theoretic approach is that it allows us to construct $p$-adic families of Galois representations lifting the actual representation $\bar{\rho }$, and not just the semisimplification.

19 pages. Final version, to appear in the IJNT

References in corpus (2)

• Deformations of Galois representations and exceptional monodromy
• Constructing Certain Special Analytic Galois Extensions