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Let $X$ be a quasi-compact and quasi-separated scheme, and $U\subseteq X$ be a quasi-compact open subscheme. Then we can consider $Rj_*\mathcal{O}_U$ the (derived) pushforward of the structure sheaf of $U$. This is a coconnective sheaf of rings (in fact it is locally of Tor amplitude in $(-∞,0]$, since locally it can be represented as a finite limit of sheaves of the form $\mathcal{O}_X[f^{-1}]$).

Q: Can $Rj_*\mathcal{O}_U$ be represented as a filtered colimit of uniformly bounded below perfect complexes?

Note: I am using the homological grading convention, so, e.g., for me every connective sheaf is bounded below.

The result is true if $X$ has an ample family of line bundles, because then I could just use the colimit of Koszul complexes, but I'd like it to be true in more generality.

Let $X$ be a quasi-compact and quasi-separated scheme, and $U\subseteq X$ be a quasi-compact open subscheme. Then we can consider $Rj_*\mathcal{O}_U$ the (derived) pushforward of the structure sheaf of $U$. This is a coconnective sheaf of rings (in fact it is locally of Tor amplitude in $(-∞,0]$, since locally it can be represented as a finite limit of sheaves of the form $\mathcal{O}_X[f^{-1}]$).

Q: Can $Rj_*\mathcal{O}_U$ be represented as a filtered colimit of uniformly bounded above perfect complexes?

Note: I am using the homological grading convention, so, e.g., for me every connective sheaf is bounded below.

The result is true if $X$ has an ample family of line bundles, because then I could just use the colimit of Koszul complexes, but I'd like it to be true in more generality.

Let $X$ be a quasi-compact and quasi-separated scheme, and $U\subseteq X$ be a quasi-compact open subscheme. Then we can consider $Rj_*\mathcal{O}_U$ the (derived) pushforward of the structure sheaf of $U$. This is a coconnective sheaf of rings (in fact it is locally of Tor amplitude in $(-∞,0]$, since locally it can be represented as a finite limit of sheaves of the form $\mathcal{O}_X[f^{-1}]$).

Q: Can $Rj_*\mathcal{O}_U$ be represented as a filtered colimit of uniformly bounded perfect complexes?

Note: I am using the homological grading convention, so for me every coconnective sheaf is bounded above.

The result is true if $X$ has an ample family of line bundles, because then I could just use the colimit of Koszul complexes, but I'd like it to be true in more generality.

Let $X$ be a quasi-compact and quasi-separated scheme, and $U\subseteq X$ be a quasi-compact open subscheme. Then we can consider $Rj_*\mathcal{O}_U$ the (derived) pushforward of the structure sheaf of $U$. This is a coconnective sheaf of rings (in fact it is locally of Tor amplitude in $(-∞,0]$, since locally it can be represented as a finite limit of sheaves of the form $\mathcal{O}_X[f^{-1}]$).

Q: Can $Rj_*\mathcal{O}_U$ be represented as a filtered colimit of uniformly bounded below perfect complexes?

Note: I am using the homological grading convention, so, e.g., for me every connective sheaf is bounded below.

The result is true if $X$ has an ample family of line bundles, because then I could just use the colimit of Koszul complexes, but I'd like it to be true in more generality.

Let $X$ be a quasi-compact and quasi-separated scheme, and $U\subseteq X$ be a quasi-compact open subscheme. Then we can consider $Rj_*\mathcal{O}_U$ the (derived) pushforward of the structure sheaf of $U$. This is a coconnective sheaf of rings (in fact it is locally of Tor amplitude in $(-∞,0]$, since locally it can be represented as a finite limit of sheaves of the form $\mathcal{O}_X[f^{-1}]$).

Q: Can $Rj_*\mathcal{O}_U$ be represented as a filtered colimit of uniformly bounded above perfect complexes?

Note: I am using the homological grading convention, so for me every coconnective sheaf is bounded above.

The result is true if $X$ has an ample family of line bundles, because then I could just use the colimit of Koszul complexes, but I'd like it to be true in more generality.

Let $X$ be a quasi-compact and quasi-separated scheme, and $U\subseteq X$ be a quasi-compact open subscheme. Then we can consider $Rj_*\mathcal{O}_U$ the (derived) pushforward of the structure sheaf of $U$. This is a coconnective sheaf of rings (in fact it is locally of Tor amplitude in $(-∞,0]$, since locally it can be represented as a finite limit of sheaves of the form $\mathcal{O}_X[f^{-1}]$).

Q: Can $Rj_*\mathcal{O}_U$ be represented as a filtered colimit of uniformly bounded perfect complexes?

Note: I am using the homological grading convention, so for me every coconnective sheaf is bounded above.

The result is true if $X$ has an ample family of line bundles, because then I could just use the colimit of Koszul complexes, but I'd like it to be true in more generality.