The derived category of quasi-coherent sheaves and axiomatic stable homotopy
Alonso, Leovigildo ; Jeremias, Ana ; Perez, Marta ; Vale, Maria J.
arXiv, 0706.0493 / Harvested from arXiv
Text on arXiv
We prove in this paper that for a quasi-compact and semi-separated (non necessarily noetherian) scheme X, the derived category of quasi-coherent sheaves over X, D(A_qc(X)), is a stable homotopy category in the sense of Hovey, Palmieri and Strickland, answering a question posed by Strickland. Moreover we show that it is unital and algebraic. We also prove that for a noetherian semi-separated formal scheme X, its derived category of sheaves of modules with quasi-coherent torsion homologies D_qct(X) is a stable homotopy category. It is algebraic but if the formal scheme is not a usual scheme, it is not unital, therefore its abstract nature differs essentially from that of the derived category of a usual scheme.
Publié le : 2007-06-04
Classification:  Mathematics - Algebraic Geometry,  Mathematics - Algebraic Topology,  14F99 (Primary), 14F05, 18E30 (Secondary) 
@article{0706.0493,
     author = {Alonso, Leovigildo and Jeremias, Ana and Perez, Marta and Vale, Maria J.},
     title = {The derived category of quasi-coherent sheaves and axiomatic stable
  homotopy},
     journal = {arXiv},
     volume = {2007},
     number = {0},
     year = {2007},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0706.0493}
}

Alonso, Leovigildo; Jeremias, Ana; Perez, Marta; Vale, Maria J. The derived category of quasi-coherent sheaves and axiomatic stable
  homotopy. arXiv, Tome 2007 (2007) no. 0, . http://gdmltest.u-ga.fr/item/0706.0493/