A Tensor-Triangulated Approach to Derived Categories of Non-Noetherian Rings

Abstract

We investigate the subcategories and Bousfield lattices of derived categories of general commutative rings, extending previous work done under a Noetherian hypothesis. Maps between rings R → S induce adjoint functors between unbounded derived categories D(R) → D(S), and we explore the induced relationships between thick and localizing subcategories, and Bousfield lattices. Several specific non-Noetherian rings are studied in depth. We also contextualize these results within the human dimension in which they occurred.