Galois representations and composite moduli

2021/05/24 by Subham Bhakta, Bhakta, Subham
Arts and Humanities · Mathematics · #11F80 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Historical Studies and Socio-cultural Analysis #Number Theory (math.NT) #Primary 11G05 #Secondary 20G30

paper · pdf · doi:10.48550/arxiv.2105.11230

openalex publication_date 2021/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is known that for any elliptic curve E/ℚ and any integer m co-prime to 30, the induced Galois representation ρ_E,m: Gal(ℚ/ℚ) \longrightarrow GL₂(ℤ/mℤ) is surjective if and only if ρ_E,ℓ is surjective for any prime ℓ|m. In this article, we shall discuss some generalizations, applications, and variants of this phenomenon.

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