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Pro-$l$ Sylow action in a primitive representation of inertia over $\overline{\mathbb{F}}_l$
Let $K$ be a nonarchimedean local field of residue characteristic $p \neq l$ and let $I_K$ be the inertia subgroup of its absolute Galois group. Let $V$ an irreducible representation of $I_K$ over $\...
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