English

Transcendental l-adic Galois representations

Number Theory 2007-05-23 v1

Abstract

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.

Keywords

Cite

@article{arxiv.math/0404254,
  title  = {Transcendental l-adic Galois representations},
  author = {Chandrashekhar Khare and Michael Larsen and Ravi Ramakrishna},
  journal= {arXiv preprint arXiv:math/0404254},
  year   = {2007}
}

Comments

21 pages