Constructing semisimple p-adic Galois representations with prescribed properties

Khare, Chandrashekhar; Larsen, Michael; Ramakrishna, Ravi

Constructing semisimple p-adic Galois representations with prescribed properties

Authors

Khare, Chandrashekhar

Larsen, Michael

Ramakrishna, Ravi

Description

In this paper we show that two dimensional (mod p) Galois representations satisfying mild hypotheses can be lifted to p-adic Galois representations ramified at infinitely many primes such that the characteristic polynomials of Frobenius at a density one set of unramified primes are defined over the rational integers. In particular we show that often one can "density one compatibly" lift mod p and mod q Galois representations.
32 pages