Given a genus two hyperelliptic curve over a totally real field , we show that the mod Galois representation attached to is residually automorphic when the image of is isomorphic to and it is also a transitive subgroup under a fixed isomorphism . More precisely, there exists a Hilbert–Siegel Hecke eigen cusp form on of parallel weight two whose mod Galois representation is isomorphic to .
Soit une courbe hyperelliptique de genre sur un corps totalement réel . Nous montrons que la représentation galoisienne modulo , associée à est résiduellement automorphe lorsque l’image de est un groupe isomorphe à et transitif par rapport à un isomorphisme fixé . Plus précisément, il existe une forme parabolique de Hilbert–Siegel sur de poids parallèle , propre pour les opérateurs de Hecke, dont la représentation galoisienne est isomorphe à .
Revised:
Accepted:
Published online:
Keywords: genus 2 curves, mod 2 Galois representations, automorphy
Alexandru Ghitza 1; Takuya Yamauchi 2
@article{JTNB_2024__36_2_637_0, author = {Alexandru Ghitza and Takuya Yamauchi}, title = {Automorphy of mod~2 {Galois} representations associated to certain genus 2 curves over totally real fields}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {637--660}, publisher = {Soci\'et\'e Arithm\'etique de Bordeaux}, volume = {36}, number = {2}, year = {2024}, doi = {10.5802/jtnb.1291}, language = {en}, url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1291/} }
TY - JOUR AU - Alexandru Ghitza AU - Takuya Yamauchi TI - Automorphy of mod 2 Galois representations associated to certain genus 2 curves over totally real fields JO - Journal de théorie des nombres de Bordeaux PY - 2024 SP - 637 EP - 660 VL - 36 IS - 2 PB - Société Arithmétique de Bordeaux UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1291/ DO - 10.5802/jtnb.1291 LA - en ID - JTNB_2024__36_2_637_0 ER -
%0 Journal Article %A Alexandru Ghitza %A Takuya Yamauchi %T Automorphy of mod 2 Galois representations associated to certain genus 2 curves over totally real fields %J Journal de théorie des nombres de Bordeaux %D 2024 %P 637-660 %V 36 %N 2 %I Société Arithmétique de Bordeaux %U https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1291/ %R 10.5802/jtnb.1291 %G en %F JTNB_2024__36_2_637_0
Alexandru Ghitza; Takuya Yamauchi. Automorphy of mod 2 Galois representations associated to certain genus 2 curves over totally real fields. Journal de théorie des nombres de Bordeaux, Volume 36 (2024) no. 2, pp. 637-660. doi : 10.5802/jtnb.1291. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1291/
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