most recent 30 from http://mathoverflow.net 2013-05-24T05:23:09Z http://mathoverflow.net/feeds/question/99689 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/99689/existence-of-dg-realization-for-6-functors kazhdan david 2012-06-15T10:20:56Z 2012-11-27T07:53:39Z

<p>Is there a way to lift 6 functors on constructable sheaves to the dg world?</p>

http://mathoverflow.net/questions/99689/existence-of-dg-realization-for-6-functors/100560#100560 Liz Wood 2012-06-25T03:31:48Z 2012-06-25T03:31:48Z

<p>Yes, not just presumably but definitively.</p>

http://mathoverflow.net/questions/99689/existence-of-dg-realization-for-6-functors/100570#100570 DamienC 2012-06-25T07:45:08Z 2012-11-27T07:53:39Z

<p>If I understand correctly your are looking for a dg enhancement of the six operation formalism. </p> <p>There seem to be a paper that does something very close to it: Yifeng Liu and Weizhe Zheng, <em>Enhanced six operations and base change theorem for sheaves on Artin stacks</em> (available at <a href="http://math.columbia.edu/~liuyf/sixi.pdf" rel="nofollow">http://math.columbia.edu/~liuyf/sixi.pdf</a>). </p> <p>They use the language of $(\infty,1)$-categories, but I think one can adapt it to dg-categories (assuming that one is working over a field of characteristic zero). </p> <p>EDIT Nov. 27, 2012: the above preprint has been posted on the arXiv: <a href="http://arxiv.org/abs/1211.5948" rel="nofollow">http://arxiv.org/abs/1211.5948</a></p>