Classifying thick subcategories of the stable category of Cohen-Macaulay modules – University of Copenhagen

Classifying thick subcategories of the stable category of Cohen-Macaulay modules

Specialeforsvar ved Kristian Peter Poulsen

Titel: Classifying thick subcategories of the stable category of Cohen-Macaulay modules 

 

Abstract: This thesis deals with a classification of the thick subcategories of stable category of the category of maximal Cohen-Macaulay modules. Letting the ring R be an abstract hypersurface there is a one-to-one correspondence between the thick subcategories of MCM(R) and the specialization-closed subsets of prime ideals p of R such that R_p is not regular. We start out by building the theoretical foundation. That is, we study the localization property, notions about dimension and depth, and we investigate the additively, the extensions-closed and the resolving subcategories of modR. Further we study the nonfree loci V(X) and V(\X) of an R-module and a subcategory \X of mod R, respectively. We prove a first version of the correspondence result where we over a Cohen-Macaulay local ring R look at the thick subcategories \X of MCM(R) with certain restrictions. We then improve the result by letting the ring R be an abstract hypersurface. In the end we transfer the result to the stable category of MCM(R). 

 

Vejleder:  Henrik G. Holm
Censor:    Niels Lauritzen, Aarhus Universitet