On the Image of the Totaling Functor

Details On the Image of the Totaling Functor On the Image of the Totaling Functor

2011-05-19

arxiv.org/abs/1105.3869v1

Mathematics

Category Theory

21 pages; comments welcome

Scientific paper

Let A be a polynomial ring in d variables over a field. In this paper, we investigate the image of the totaling functor between the derived category of graded A-modules and the derived category of DG A-modules. In particular, we show that when d is at least two, there exist semifree DG modules of rank at least four which are not quasiisomorphic to the totaling of a complex of graded A-modules. However, when d=1 we show that the totaling functor is onto. Moveover, when A is an arbitrary DG algebra with trivial differential, we exhibit a special class of semifree DG modules over A which are always equal to the totaling of some complex of graded A-modules.

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