Constructing semisimple p-adic galois representations with prescribed properties

Consider a characteristic p representation of the absolute Galois group of the rational numbers. In this paper we show how to deform this representation to the p-adics while guaranteeing that the characteristic polynomials of Frobenius at a density one set of primes are algebraic and pure of specified weight. The resulting representation is ramified at an infinite (density zero) set of primes. As a consequence of the technique of proof we show that one can compatibly lift a mod pq representation. Again, the resulting representation is ramified at infinitely many primes.