2
$\begingroup$

Let $X$ be a scheme. Let $E$ be a perfect complex of coherent sheaves on $X$ and suppose it admits two global resolutions $ F$ and $F'$. By global resolution I mean that both $F$ and $F'$ are quasi-isomorphic to $E$ and both are complexes of vector bundles.

$\bf{Question:}$ Is it possible to find a global resolution $H$ of $E$ such that $ F, F'$ map mono-morphically into $H$?

I know how to do this when $E$ has perfect amplitude $[0, 1]$ but I don't see how to generalize to say $[0, n]$ for arbitrary $n$.

$\endgroup$
  • $\begingroup$ Why do you want this? $\endgroup$ – Sasha Jan 12 at 7:21

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Browse other questions tagged or ask your own question.