Finiteness of Selmer groups and deformation rings
  We prove the finiteness of Selmer groups attached to lifts of certain 2-dimensional mod p representations of the absolute Galois group of Q. The mod p representation can be either even or odd. The lifts considered are the ones that were proven to exist by the seond named author. 
Chandrashekhar Khare and Ravi Ramakrishna