most recent 30 from http://mathoverflow.net 2013-05-25T05:26:09Z http://mathoverflow.net/feeds/question/48407 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/48407/derived-category-of-equivariant-coherent-sheaves-and-fixed-points Hiraku Nakajima 2010-12-06T00:09:13Z 2010-12-06T00:09:13Z

<p>The K-group $K^T(X)$ of $T$(torus)-equivariant coherent sheaves on a variety $X$ is isomorphic to $K^T(X^T)$, that of the fixed point locus via the inclusion homomorphism, when we tensor the quotient field of the representation ring $R(T)$ of $T$. </p> <p>Is there a similar result for $D_T(Coh X)$ and $D_T(Coh X^T)$, derived categories of $T$-equivariant coherent sheaves ? I do not know even how to formulate `the quotient field of $R(T)$' in the derived category case.</p>