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.