Transcendental l-adic Galois representations

Khare, Chandrashekhar; Larsen, Michael; Ramakrishna, Ravi

Transcendental l-adic Galois representations

Authors

Khare, Chandrashekhar

Larsen, Michael

Ramakrishna, Ravi

Description

We consider continuous representations of the Galois group G of a number field K taking values in the completion C of an algebraic closure A of the field of l-adic numbers. We give a construction of irreducible representations of G in GL(2,C) which cannot be conjugated into GL(2,A) but for which there exist density-one sets of primes with Frobenius traces in A. We also show that any such representation must be ramified at infinitely many primes of K.
21 pages