Bousfield localization on formal schemes

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Let (X, O_X) be a noetherian formal scheme and consider D_qct(X) its derived category of sheaves with quasi-coherent torsion homology. We show that there is a bijection between the set of rigid (i.e. \tensor-ideals) localizing subcategories of D_qct(X) and subsets in X, generalizing previous work by Neeman. If moreover X is separated, the associated localization and acyclization functors are described in certain cases. When Z is a stable for specialization subset of X, its associated acyclization is Γ_Z. When X is an scheme, the corresponding localizing subcategories are generated by perfect complexes and we recover Thomason's classification of thick subcategories. On the other hand, if Y is a generically stable subset of X, we give an expression for the associated localization functor.
Relaxed the separation hypothesis. Added connection with Thomason's classification of thick subcategories

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Algebraic Geometry, Algebraic Topology, 14F99; 14F05, 18E30

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http://salesiana.dossiersoluciones.com/handle/123456789/68068

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0307189
 http://arxiv.org/abs/math/0307189

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arXiv