论文标题
Mod 2 Galois表示的自动形式与某些属2曲线相关的完全真实领域
Automorphy of mod 2 Galois representations associated to certain genus 2 curves over totally real fields
论文作者
论文摘要
让$ c $成为一个完全真实的场上$ f $的两属双层次曲线。我们表明mod 2 galois表示$ \barρ_{同构至$ s_5 $，它也是固定同构$ \ mathrm {gsp} _2（\ mathbb {f} _2）\ cong s_6 $下的固定同构中的及物子组。更确切地说，存在于$ \ mathrm {gsp} _4（\ Mathbb {a} _f）的hilbert-siegel hecke egke eigen cusp表格，平行重量二的mod 2 galois表示为$ \barρ_{c，c，2} $。
Let $C$ be a genus two hyperelliptic curve over a totally real field $F$. We show that the mod 2 Galois representation $\barρ_{C,2}\colon\mathrm{Gal}(\bar{F}/F)\to \mathrm{GSp}_4(\mathbb{F}_2)$ attached to $C$ is automorphic when the image of $\barρ_{C,2}$ is isomorphic to $S_5$ and it is also a transitive subgroup under a fixed isomorphism $\mathrm{GSp}_2(\mathbb{F}_2)\cong S_6$. To be more precise, there exists a Hilbert--Siegel Hecke eigen cusp form on $\mathrm{GSp}_4(\mathbb{A}_F)$ of parallel weight two whose mod 2 Galois representation is isomorphic to $\barρ_{C,2}$.
