WARNING: The image types of nonmaximal primes is still in development, and subject to change.

Let $p$ be a prime and let $C$ be a 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-Semistable **nss**, and last but very much not least, the super duper mysterious and esoteric unknown type **?**. Can you catch 'em all?

**Authors:**

**Knowl status:**

- Review status: beta
- Last edited by David Roe on 2021-10-13 23:17:33

**Referred to by:**

Not referenced anywhere at the moment.

**History:**(expand/hide all)

- 2021-10-13 23:17:33 by David Roe
- 2020-12-07 07:26:48 by Barinder Banwait
- 2020-12-05 13:42:08 by Barinder Banwait
- 2020-11-18 06:35:23 by Barinder Banwait
- 2020-11-18 06:22:16 by Barinder Banwait

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