We develop a theory of cosupport and costratification in tensor triangular geometry. We
study the geometric relationship between support and cosupport, provide a conceptual …

Students of mathematics learn how to complete the rational numbers Q using the distance
metric in order to obtain the real numbers R (see eg [24, Chap. 2]). In lectures on number …

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 …

Let a be an ideal of a commutative Noetherian (not necessarily local) ring R. In the case cd
(a, R)≤ 1, we show that the subcategory of a-cofinite R-modules is Abelian. Using this fact …

This thesis is comprised of three chapters. The first chapter deals with bounded complexes
of Gorenstein projective and Gorenstein injective modules. Deploying methods of relative …

We introduce a new class of commutative noetherian DG-rings which generalizes the class
of regular local rings. These are defined to be local DG-rings (A, m¯) such that the maximal …

The extension of scalars functor along a finite ring homomorphism is a classic example of a
functor which preserves purity and pure injectivity. We consider how this functor behaves …

We show that the cosupport of a commutative noetherian ring is precisely the set of primes
appearing in a minimal pure-injective resolution of the ring. As an application of this, we …

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 …