Deformations of certain reducible Galois representations III

Abstract

Let [Formula: see text] be an odd prime and [Formula: see text] a power of [Formula: see text]. We examine the deformation theory of reducible and indecomposable Galois representations [Formula: see text] that are unramified outside a finite set of primes [Formula: see text] and whose image lies in a Borel subgroup. We show that under some additional hypotheses, such representations have geometric lifts to the Witt vectors [Formula: see text]. The main theorem of this paper is a higher-dimensional generalization of the result of [S. Hamblen and R. Ramakrishna, Deformations of certain reducible Galois II, Amer. J. Math. 130(4) (2008) 913–944] [5].