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user127776
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Cohomological dimension of continuous étale cohomology of twisted powers of roots of unity

Given a finitely generated field $F$ of char $p$, consider the continuous étale cohomology $H^{i,p}=H_{cont}^i(F, (\mu^{\otimes p}_{l^n}))\otimes \mathbb{Q}$ where $l$ is an invertible prime. The contiuous étale cohomology of a field is defined as the direct limit of continuous étale cohomology of open subvarieties of the variety that its function field is $F$. Why $H^{i,p}$ is zero for $i>p+1$ regardless of the transcendental degree of $F$?

user127776
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