Bousfield localization on formal schemes

Details Bousfield localization on formal schemes Bousfield localization on formal schemes

2003-07-14

arxiv.org/abs/math/0307189v2

Mathematics

Algebraic Geometry

Relaxed the separation hypothesis. Added connection with Thomason's classification of thick subcategories

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Bousfield localization on formal schemes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Bousfield localization on formal schemes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Bousfield localization on formal schemes will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-381994