most recent 30 from http://mathoverflow.net 2013-05-22T20:09:09Z http://mathoverflow.net/feeds/question/86175 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/86175/fiber-functors-to-derived-categories Rebecca Bellovin 2012-01-20T06:57:16Z 2012-01-20T06:57:16Z

<p>Suppose that $G$ is an algebraic group over a field $k$. Then for any $k$-algebra $R$, a fiber functor from $\text{Rep}_k(G)$ to the category of projective modules over $R$ is the same as a $G$-torsor on $\text{Spec}(R)$, by Theorem 3.2 of Deligne-Milne.</p> <p>Now suppose that instead of a $k$-linear faithful exact tensor functor into the category of projective modules, I have a functor (taking exact sequences of representations to distinguished triangles, and $\otimes$ to $\otimes^L$, say) to the bounded derived category of coherent modules over $R$. Do I get some sort of "derived $G$-bundle" on $\text{Spec}(R)$? What should that mean?</p>