Automorphy of mod 2 Galois representations associated to certain genus 2 curves over totally real fields

2020/10/18 by Ghitza, Alexandru, Yamauchi, Takuya · 1 citation
#11F33 #11F80 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2010.10021

Abstract

Let C be a genus two hyperelliptic curve over a totally real field F. We show that the mod 2 Galois representation ρ_C,2\colonGal(F/F)→ GSp₄(\mathbbF₂) attached to C is automorphic when the image of ρ_C,2 is isomorphic to S₅ and it is also a transitive subgroup under a fixed isomorphism GSp₂(\mathbbF₂)≅ S₆. To be more precise, there exists a Hilbert--Siegel Hecke eigen cusp form on GSp₄(\mathbbA_F) of parallel weight two whose mod 2 Galois representation is isomorphic to ρ_C,2.

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