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S. Carnahan ♦
S. Carnahan ♦
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Let F=(F_n)n be an l-adic sheaf on X{et}$F=(F\_n)\_n$ be an $\ell$-adic sheaf on $X\_{et}$, for a variety X$X$ over an algebraically closed field k$k$ of characteristic not equal to l$\ell$. Does the presheaf sending U$U$ to H^i(U,F):=\lim_nH^i(U,F_n)$H^i(U,F):=\lim\_n H^i(U,F\_n)$ sheafify to zero?

Let F=(F_n)n be an l-adic sheaf on X{et}, for a variety X over an algebraically closed field k of characteristic not equal to l. Does the presheaf sending U to H^i(U,F):=\lim_nH^i(U,F_n) sheafify to zero?

Let $F=(F\_n)\_n$ be an $\ell$-adic sheaf on $X\_{et}$, for a variety $X$ over an algebraically closed field $k$ of characteristic not equal to $\ell$. Does the presheaf sending $U$ to $H^i(U,F):=\lim\_n H^i(U,F\_n)$ sheafify to zero?

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shenghao
shenghao
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sheafifying a projective limit of presheaves

Let F=(F_n)n be an l-adic sheaf on X{et}, for a variety X over an algebraically closed field k of characteristic not equal to l. Does the presheaf sending U to H^i(U,F):=\lim_nH^i(U,F_n) sheafify to zero?