Hovey, Palmieri and Strickland have defined the concept of stable homotopy
category in [HPS]. It consists of a list of additional properties and structure for a triangu-
lated category. This concept arises in several contexts of algebraic geometry and topology,
being two essential examples, D(R), the derived category of complexes of modules over a
commutative ring R, and HoSp, the category of (non-connective) spectra up to homotopy.

In this talk we will show that for a quasi-compact and semi-separated (non necessarily
noetherian) scheme X, the derived category of quasi-coherent sheaves over X, D(Aqc(X)),
is a stable homotopy category. We will also deal with the analogous result for formal
schemes, namely, if X is a noetherian semi-separated formal scheme the derived category of
sheaves with quasi-coherent torsion homologies, Dqct(X) (cfr. [AJL]), is a stable homotopy
category. These results are included in [AJPV].

References
[AJL] Alonso Tarrío, L.; Jeremías López, A.; Lipman, J.: Duality and
flat base change on formal schemes,
in Studies in duality on noetherian formal schemes and non-noetherian ordinary schemes. Providence, RI:
American Mathematical Society. Contemp. Math. 244, 3-90 (1999).
[AJPV] Alonso Tarrío, L.; Jeremías López, A.; Pérez Rodríguez, M.; Vale Gonsalves, M. J.: The derived
category of quasi-coherent sheaves and axiomatic stable homotopy. Advances in Mathematics 218, 1224-
1252 (2008).
[HPS] Hovey, M.; Palmieri, J. H.; Strickland, N. P.: Axiomatic stable homotopy theory. Mem. Amer. Math.
Soc. 128 (1997), no. 610