Homological algebra originated in late 19th century topology. Homological studies of
algebraic objects, such as rings and modules, only got under way in the middle of the 20th …

Over a commutative noetherian ring R of finite Krull dimension, we show that every complex
of flat cotorsion R-modules decomposes as a direct sum of a minimal complex and a …

We develop the theory of costratification in the setting of relative tensor-triangular geometry,
in the sense of Stevenson, providing a unified approach to classification results of Neeman …

Let R be a commutative noetherian ring. We give criteria for a complex of cotorsion flat R-
modules to be minimal, in the sense that every self homotopy equivalence is an …

Let R be a commutative Noetherian ring. We introduce the notion of localization functors λ W
with cosupports in arbitrary subsets W of Spec R; it is a common generalization of …

We prove that any affine ring R over a field k has full cosupport, ie, the cosupport of R is
equal to Spec R. Using this fact, we give a complete description of all terms in a minimal …

In Chapter 2, we compute a semi-free resolution of the Koszul complex over its
endomorphism ring. This computation leads to an expression of the local cohomology of a …

In the 1960s, Grothendieck introduced the notion of local cohomology from the viewpoint of
geometry. It has brought great benefits to commutative algebra, and has been an essential …