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for questions about etale cohomology of schemes, including foundational material and applications.

4 votes
0 answers
273 views

nearby cycles map for affine formal schemes

Assume that $X=Spf R$ is p-adic formal scheme over $O_{C_p}$ with generic fiber $X_{\eta}$. I want to know why the nearby cycles map $Ru^\star \mathbb{Z/p}$ is equal to $R\Gamma_{et}(spec R[1/p],\math …
6 votes
0 answers
242 views

Computing Hodge numbers by point counting

In the lecture note of Bhatt from Arizona winter school 2017, there is an exercise which claims if X is a proper smooth scheme defined over $\mathbb{Z}[1/N]$ and if there is a polynomial $P$ such that …