Bousfield localization on formal schemes
摘要
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 \Gamma_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.
引用
@article{arxiv.math/0307189,
title = {Bousfield localization on formal schemes},
author = {Leovigildo Alonso and Ana Jeremias and Ma. -Jose Souto},
journal= {arXiv preprint arXiv:math/0307189},
year = {2007}
}
备注
Relaxed the separation hypothesis. Added connection with Thomason's classification of thick subcategories