Galois representations and composite moduli

Subham Bhakta

Galois representations and composite moduli

Number Theory 2023-01-04 v2

Authors: Subham Bhakta

Abstract

It is known that for any elliptic curve $E/\mathbb{Q}$ and any integer $m$ co-prime to $30,$ the induced Galois representation $\rho_{E,m}: \text{Gal}(\overline{\mathbb{Q}}/\mathbb{Q}) \longrightarrow \text{GL}_{2}(\mathbb{Z}/m\mathbb{Z})$ is surjective if and only if $\rho_{E,\ell}$ is surjective for any prime $\ell|m.$ In this article, we shall discuss some generalizations, applications, and variants of this phenomenon.

Keywords

galois representations galois theory elliptic curves

Cite

@article{arxiv.2105.11230,
  title  = {Galois representations and composite moduli},
  author = {Subham Bhakta},
  journal= {arXiv preprint arXiv:2105.11230},
  year   = {2023}
}

Comments

The title is modified, and the abstract is updated. A few arguments are rephrased

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