Congruences between modular forms modulo prime powers

摘要

Given a prime p = 5 and an abstract odd representation rho(n) with coefficients modulo p(n) (for some n = 1) and big image, we prove the existence of a lift of rho(n) to characteristic 0 whenever local lifts exist (under minor technical conditions). Moreover, our results allow to chose the lift's inertial type at all primes but finitely many (where the lift is of Steinberg type).