The derived category of quasi-coherent sheaves and axiomatic stable homotopy |
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Authors: | Leovigildo Alonso Tarrío Ana Jeremías López |
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Institution: | a Departamento de Álxebra, Facultade de Matemáticas, Universidade de Santiago de Compostela, E-15782 Santiago de Compostela, Spain b Departamento de Matemáticas, Esc. Sup. de Enx. Informática, Campus de Ourense, Universidade de Vigo, E-32004 Ourense, Spain |
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Abstract: | 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, D(Aqc(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 Dqct(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 Dqc(X) (which is equivalent to D(Aqc(X))) in the case of a usual scheme. |
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Keywords: | primary 14F99 secondary 14F05 18E30 |
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