标题： 虚二次域上伽罗瓦表示的形变问题 显示英文标题

标题： A deformation problem for Galois representations over imaginary quadratic fields

摘要： 我们证明了在某些假设下，虚二次域F上的最小分歧的普通残余可约p进伽罗瓦表示的模性。 我们首先展示在何种条件下，残余表示在同构意义下是唯一的。 然后我们通过泰勒等人构造的伽罗瓦表示，证明了来自GL_2(A_F)上尖形式的形变的存在性。 我们建立了一个充分条件（以某些域扩张的不存在性为条件，而在许多情况下可以简化为关于L值的条件），使得普遍形变环是一个离散赋值环，在这种情况下我们证明了一个R=T定理。 我们还研究了可约形变，并证明不存在最小的特征0可约形变。 显示英文摘要

摘要： We prove the modularity of minimally ramified ordinary residually reducible p-adic Galois representations of an imaginary quadratic field F under certain assumptions. We first exhibit conditions under which the residual representation is unique up to isomorphism. Then we prove the existence of deformations arising from cuspforms on GL_2(A_F) via the Galois representations constructed by Taylor et al. We establish a sufficient condition (in terms of the non-existence of certain field extensions which in many cases can be reduced to a condition on an L-value) for the universal deformation ring to be a discrete valuation ring and in that case we prove an R=T theorem. We also study reducible deformations and show that no minimal characteristic 0 reducible deformation exists.