  For a representation of the absolute Galois group of the rationals over a
finite field of characteristic $p$, we study the existence of a lift to
characteristic zero that is geometric in the sense of the Fontaine-Mazur
conjecture. For two-dimensional representations, Ramakrishna proved that under
technical assumptions odd representations admit geometric lifts. We generalize
this to higher dimensional orthogonal and symplectic representations. A key
step is generalizing and studying a local deformation condition at $p$ arising
from Fontaine-Laffaille theory.
