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Let $\pi:X\rightarrow Y$ a Galois cover of finite type schemes over $\mathbb{C}$ of group $\Gamma$.

Let $n$ an integer such that it is not prime with the order of $\Gamma$. Then $\pi_{*}\mathbb{Z}/n\mathbb{Z}$ is perverse with a $\Gamma$-action.

If I take derived invariants for $\Gamma$, is it true that the sheaf is still perverse?

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