Galois representations with big image in the general symplectic group $\operatorname{GSp}_4(\mathbb{Z}_p)$

Simone Maletto

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arXiv · 2208.11049

Galois representations with big image in the general symplectic group $\operatorname{GSp}_4(\mathbb{Z}_p)$

Simone Maletto

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Abstract

Let $p$ be an odd prime and $e_p$ be its irregularity index. If $4e_p+8 <\frac{p-1}{2}$ we construct a Galois representation with image in the diagonal torus of $\op{GSp}_4(\Fp)$ that lifts to a characteristic $0$ representation unramified at all primes $\ell\neq p$ with image containing a finite index subgroup of $\Symp$.

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Simone Maletto. 2022-08-23. Galois representations with big image in the general symplectic group $\operatorname{GSp}_4(\mathbb{Z}_p)$. https://arxiv.org/abs/2208.11049

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