Blowing up a derived scheme - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-25T00:24:03Z http://mathoverflow.net/feeds/question/81773 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/81773/blowing-up-a-derived-scheme Blowing up a derived scheme Josh Shadlen 2011-11-24T02:55:16Z 2011-11-29T03:41:02Z <p>Is there a sensible notion of blowing up in any of the available frameworks for derived algebraic geometry? I am happy to remain in the affine setting, where I think the right question to ask is "what does it mean to take powers of an ideal?" in say, a commutative differential graded algebra.</p> http://mathoverflow.net/questions/81773/blowing-up-a-derived-scheme/82138#82138 Answer by Sean Sather-Wagstaff for Blowing up a derived scheme Sean Sather-Wagstaff 2011-11-29T03:41:02Z 2011-11-29T03:41:02Z <p>I assume that you're working in the DG category, so I take "ideal" to mean "DG ideal". Let $R$ be a commutative DG algebra and $I$ an ideal of $R$. Then for each $n\geq 1$, I set $I^n$ equal to the intersection of all the DG ideals of $R$ that contain the set $S(n)$ consisting of all elements of the form $a_1\cdots a_n$ such that $a_1,\ldots,a_n\in I$. In other words, $I^n$ is the DG ideal of $R$ generated by $S(n)$. </p>