• Corpus ID: 221265978

Automorphy of mod 2 Galois representations associated to the quintic Dwork family and reciprocity of some quintic trinomials

@article{Tsuzuki2020AutomorphyOM,
  title={Automorphy of mod 2 Galois representations associated to the quintic Dwork family and reciprocity of some quintic trinomials},
  author={Nobuo Tsuzuki and Takuya Yamauchi},
  journal={arXiv: Number Theory},
  year={2020}
}
In this paper, we determine mod $2$ Galois representations $\overline{\rho}_{\psi,2}:G_K:={\rm Gal}(\overline{K}/K)\longrightarrow {\rm GSp}_4(\mathbb{F}_2)$ associated to the mirror motives of rank 4 with pure weight 3 coming from the Dwork quintic family $$X^5_0+X^5_1+X^5_2+X^5_3+X^5_4-5\psi X_0X_1X_2X_3X_4=0,\ \psi\in K$$ defined over a number field $K$ under the irreducibility condition of the quintic trinomial $f_\psi$ below. Applying this result, when $K=F$ is a totally real field, for… 
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