The derived category of quasi-coherent sheaves and axiomatic stable homotopy

• Autores: Leovigildo Alonso Tarrío , Ana Jeremías López , Marta Pérez Rodríguez , María Jesús Vale Gonsalves
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 218, Nº 4, 2008, págs. 1224-1252
• Idioma: inglés
• DOI: 10.1016/j.aim.2008.03.011
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• Resumen

  • We prove in this paper that for a quasi-compact and semi-separated (nonnecessarily noetherian) scheme X, the derived category of quasi-coherent sheaves over 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 , its derived category of sheaves of modules with quasi-coherent torsion homologies 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 (which is equivalent to ) in the case of a usual scheme.