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Let $p$ be a prime and let $C$ be an genus 2 curve defined over $\mathbb{Q}$.

Subgroups $G$ of $\GSp(4,\F_\ell)$ that can arise as the image of the mod-$\ell$ Galois representation $\rho_{J,p}\colon {\Gal}(\overline{\mathbb{Q}}/\mathbb{Q})\to \GSp(4,\F_\ell)$ attached to the jacobian $J$ of $C$ that do not contain $\Sp(4,\F_\ell)$ are identified via the types arising from Mitchell's 1914 classification.

There are six types: Irreducible irred, Cuspidal cusp, One-plus-Three 1p3, Two-plus-Two 2p2, Non-Supersingular nss, and last but very much not least, the super duper mysterious and esoteric unknown type ?. Can you catch 'em all?

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Knowl status:
• Review status: beta
• Last edited by Barinder Singh Banwait on 2020-11-18 06:35:23
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Not referenced anywhere at the moment.

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