Comparison of semi-simplifications of Galois representations
Abstract
Let G be the absolute Galois group of a global field. Let r1 and r2 be two p-adic, finite dimensional representations of G. Then there exists a finite number of primes q such that if the characteristic polynomials of r1(Frob_q) and r2(Frob_q) are equal then r1 and r2 have isomorphic semi-semplifications and so the same L-functions. We give a method to compute a sufficient list of primes, based on the ramification and the dimension of the representations. We apply then the result to an article of B. van Geemen and J. Top where they described two representations and conjectured that they had isomorphic semisemplification.
Cite
@article{arxiv.math/0506053,
title = {Comparison of semi-simplifications of Galois representations},
author = {Loic Grenie},
journal= {arXiv preprint arXiv:math/0506053},
year = {2019}
}
Comments
12 pages The fifth version includes further corrections from the referee plus a correction of Proposition 14. The fourth version includes corrections suggested by the referee. It also eliminates the corrections made in second version. The third version corrects a stupid typo. The second version corrects an error in the first one: I had thought that the traces of the representations were enough but I was wrong, I need the characteristic polynomials of one generator per cyclic subgroup