Deformations of Certain Reducible Galois Representations, III

Abstract

Let $p$ be an odd prime and $q$ a power of $p$. We examine the deformation theory of reducible and indecomposable Galois representations $\bar{\rho }:G_{\mathbb{Q}}\to {\text{GSp}}_{2n}({\mathbb{F}}_q)$ that are unramified outside a finite set of primes $S$ and whose image lies in a Borel subgroup. We show that under some additional hypotheses, such representations have geometric lifts to the Witt vectors $\text{W}({\mathbb{F}}_q)$. The main theorem extends that of Hamblen and Ramakrishna in which the $n=1$ case was treated.

Final version, to appear in IJNT. 49 pages, relaxed hypotheses of main theorem, provided examples

References in corpus (3)

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