We investigate the geometry of Galois deformation rings in the defect zero setting but when the Taylor-Wiles hypothesis does not hold. In particular, we consider the question of whether or not the map from the local deformation ring to the global deformation ring is a local complete intersection map and the role the Taylor-Wiles hypothesis plays in this question. We exhibit an example in the context of classical weight two modular forms where this does not hold and shows that a resulting Tor algebra acts on the cohomology of a modular orbifold. This is joint work in progress with Preston Wake.[-]