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 be a commutative noetherian ring. The notion of-wide subcategories of is introduced and
studied in Matsui–Nam–Takahashi–Tri–Yen in relation to the cohomological dimension of a …

The present paper is devoted to an algebraic treatment of the joint spectral theory within the
framework of Noetherian modules over an algebra finite extension of an algebraically closed …

Let R be a commutative Noetherian ring. We introduce the notion of colocalization functors γ
W with supports in arbitrary subsets W of Spec R. If W is a specialization-closed subset, then …

Let R be a commutative noetherian ring of finite Krull dimension. In the first half of this talk,
we give a new approach to reach the pure derived category of flat R-modules. Motivated by …

LOCALIZATION FUNCTORS IN DERIVED CATEGORIES OF COMMUTATIVE
NOETHERIAN RINGS 1. Introduction This article is based on joint work Page 1 …

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 …