Classifying preaisles of derived categories of complete intersections

Let R be a commutative noetherian ring.Denote by mod R the category of finitely generated R-modules, by D b (R) the bounded derived category of mod R, and by D sg (R) the singularity category of R. The main result of this paper provides, when R is a complete intersection, a complete classification of the preaisles of D b (R) containing R and closed under direct summands, which includes as restrictions the classification of thick subcategories of D sg (R) due to Stevenson, and the classification of resolving subcategories of mod R due to Dao and Takahashi.1. Introduction 346 2. Resolving subcategories of triangulated categories 349 3. NE-loci of objects and subcategories of D(R) 358 4. Classification of certain preaisles of K(R) 365 5. Separating the resolving subcategories of D(R) 369 6. Classification of resolving subcategories and certain preaisles of D(R) 379 7. Restricting the classification of resolving subcategories of D(R) 384 Appendix A. Classification of resolving subcategories of K(R) with no use of D(Mod R) 391 Appendix B. Restricting the classification of resolving subcategories of K(R) 404 Acknowlegments 406 References 406