Tsutomu Nakamura, University of Verona
Title: Pure derived categories and big Cohen-Macaulay modules

In the first half of this talk, we give a new construction of the pure derived category of flat modules over a commutative noetherian ring with finite Krull dimension. Our approach enables us to directly know an explicit form of the pure derived category. In the second half of this talk, we make a kind of stable category of big Cohen-Macaulay modules, and connect it with the pure derived category. This connection yields a new framework to discuss Ziegler spectra for big Cohen-Macaulay modules over Cohen-Macaulay local rings having singularities. Our work is devoted to develop Puninski’s work below.

Gena Puninski, The Ziegler Spectrum and Ringel’s Quilt of the A-infinity Plane Curve Singularity, Algebras and Representation Theory 21 (2018), 419-446.