Let consider a quasicompact open $j:U\rightarrow\mathbb{A}^{\mathbb{N}}$ over a field $k$, Is there an example where $Rj_{*}\mathbb{Z}/n\mathbb{Z}$ is not constructible, where $n$ is prime to the characteristic?
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$\begingroup$ What precisely do you mean by $\mathbb{A}^{\mathbb{N}}$? $\endgroup$– Jason StarrCommented May 4, 2015 at 21:20
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$\begingroup$ $\varprojlim\mathbb{A}^{n}$ $\endgroup$– prochetCommented May 5, 2015 at 9:51
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$\begingroup$ With what transition maps? $\endgroup$– Jason StarrCommented May 5, 2015 at 10:25
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$\begingroup$ first projection $\endgroup$– prochetCommented May 5, 2015 at 14:01
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$\begingroup$ Okay, in that case, for every quasi-compact open $U$, there exists finite $n$ and an open $U_n \subseteq \mathbb{A}^n$ such that $U$ is the inverse image of $U_n$ under projection from $\mathbb{A}^{\mathbb{N}}$ to $\mathbb{A}^n$. There is a smooth base change theorem for constructible sheaves . . . $\endgroup$– Jason StarrCommented May 5, 2015 at 14:12
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