The splitting field of a mod-$\ell$ Galois representation $\rho:\Gal_K \to G(\F_{\ell})$ is the fixed field of the kernel of $\rho$. This is a finite Galois extension $L/K$ with $\Gal(L/K)$ isomorphic to the image of $\rho$.
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- Last edited by Andrew Sutherland on 2023-03-25 11:42:16
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