On the Liftings of 2-Dimensional Projective Galois Representations overQ Original Research Article

We show how the problem of determining the possible Artin conductors and determinant characters of liftings of a given 2-dimensional (irreducible) projective Galois representation overQcan be reduced to certain analogous local problems, and we solve those problems. By this, the problem of determining all irreducible representations of Gal(Q/Q) inGL2(C) with prescribed Artin conductor and determinant character is effectively reduced to a question in geometry of numbers.