Abstract:

In the first part of this talk, we provide a new approach to reach the pure derived category of flat modules over a commutative noetherian ring, and explain some motivation of this work from the viewpoint of replacement of objects among triangulated equivalences. In the second second part of the talk, we construct a kind of stable category of infinitely generated Cohen-Macaulay modules over a Cohen-Macaulay local ring, and discuss its property using the pure derived category. Finally, we propose a reasonable framework to continue some work by Gena Puninski about Ziegler spectra and Cohen-Macaulay representations.