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Answer by Will Sawin for Etale cohomology of relative elliptic curve

This will follow from the conjunction of three fundamental facts:(1) The pushforward of a (locally) constant $\mathbb Q_p$-sheaf along a smooth proper morphism of schemes where $p$ is invertible is...

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Etale cohomology of relative elliptic curve

Let $E_a: y^2 = x(x-1)(x-a)$ be a smooth proper relative elliptic curve over $\text{Spec}(A)$, with $a\in A$, and assume $\text{Spec}(A)$ is a $\text{Spec}(\mathbb{Q}_p)$-scheme.Let...

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