User olaf schnuerer - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T19:06:47Z http://mathoverflow.net/feeds/user/28220 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/112786/injective-dimension-of-mathcalo-x-modules Injective dimension of $\mathcal{O}_X$-modules Olaf Schnuerer 2012-11-18T20:51:19Z 2012-11-18T20:51:19Z <p>Let $(X, \mathcal{O}_X)$ be a regular noetherian scheme of finite Krull dimension (over a field $k$ if needed).</p> <p>Is it true that any $\mathcal{O}_X$-module (not necessarily quasi-coherent) has a finite resolution by injective $\mathcal{O}_X$-modules?</p> <p>This is suggested by the remark on page 136 in Hartshorne's "Residues and Duality" but I could not find a reference.</p> <p>Similarly, has any $\mathcal{O}_X$-module a finite resolution by flat $\mathcal{O}_X$-modules?</p>