most recent 30 from http://mathoverflow.net 2013-05-18T15:41:19Z http://mathoverflow.net/feeds/question/29107 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/29107/colimit-of-an-etale-diagram-of-schemes David Carchedi 2010-06-22T15:43:56Z 2010-06-22T15:43:56Z

<p>It is known that the category of schemes is not cocomplete (e.g. see this question: <a href="http://mathoverflow.net/questions/9961/colimits-of-schemes" rel="nofollow">http://mathoverflow.net/questions/9961/colimits-of-schemes</a>). However, do diagrams of schemes for which every morphism is etale have colimits? More generally, I'd really like to know if, given a scheme $X$, if the category of etale schemes over $X$ is cocomplete. I should mention that I know very little of algebraic geometry. I'm interested for "categorical reasons".</p>