On the liftings of 2-dimensional projective Galois representations over Q

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 over Q can be reduced to certain analogous local problems, and we solve those problems. By this, the problem of determining all irreducible representations of Gall ((Q) over bar/Q) in GL(2)(C) with prescribed Artin conductor and determinant character is effectively reduced to a question in geometry of numbers. (C) 1996 Academic Press, Inc.