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Bousfield localization on formal schemes

Leovigildo Alonso·Ana Jeremias·Ma. -Jose Souto
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Abstract

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.

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BibTeXRIS

Leovigildo Alonso, Ana Jeremias, Ma. -Jose Souto. 2004-02-17. Bousfield localization on formal schemes. https://arxiv.org/abs/math/0307189

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