0
$\begingroup$

Suppose $X$ is a smooth variety and consider a finite group $G$ acting on $X$. assume that the quotient map $X\rightarrow X/G$ is etale outside a codimension two subset. Suppose $H$ is coherent sheaf on $X/G$. Does there exist a finite locally free resolution for $H$ on $X/G$.

Thanks.

$\endgroup$
1
$\begingroup$

The answer is no as soon as $X/G$ is singular (which is quite often --- the simplest example is ${\mathbb C}^2/\{\pm 1\}$). You can take $H$ to be the structure sheaf of a singular point, then it does not have a finite locally free resolution.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.