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Does Riemann Hilbert correspondence commute with proper smooth pushforward?

Suppose $f:X\to Y$ is a proper smooth morphism of two analytic varieties over $\mathbb C$. Let $\mathbb L$ be a local system on $X$, I want to ask do we have $R^if_*(\mathbb L)\otimes \mathcal O_Y\sim …
2 votes
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137 views

Some questions about $\ell$-adic monodromy

I'm stucking on the proof of the Lemma 3.12 of A p-adic analogue of Borel’s theorem. Here $\mathcal A_{g,\mathrm K}$ is just a shimura variety defined over $\mathbb Z_p$, and full level $\ell$ structu …