Frobenius elements in Galois representations with SL_n image

2017/06/11 by Bisatt, Matthew
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1706.03380

Abstract

Suppose we have a elliptic curve over a number field whose mod l representation has image isomorphic to SL₂(\mathbbF_l). We present a method to determine Frobenius elements of the associated Galois group which incorporates the linear structure available. We are able to distinguish SL_n(\mathbbF_l)-conjugacy from GL_n(\mathbbF_l)-conjugacy; this can be thought of as being analogous to a result which distinguishes A_n-conjugacy from S_n-conjugacy when the Galois group is considered as a permutation group.

Related

• Identifying Frobenius elements in Galois groups
• Locally potentially equivalent two dimensional Galois representations and Frobenius fields of elliptic curves
• Comparing Galois representations in the residually reducible case
• Open image computations for elliptic curves over number fields
• Caractère d'isogénie et critères d'irréductibilité