# 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…

## One Citation

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

- Mathematics
- 2020

Let $C$ be a genus two hyperelliptic curve over a totally real field $F$. We show that the mod 2 Galois representation $\overline{\rho}_{C,2}\colon\mathrm{Gal}(\overline{F}/F)\to…

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