We study the category of matrix factorizations associated to the germ of an isolated
hypersurface singularity. This category is shown to admit a compact generator which is …

Various classification theorems of thick subcategories of a triangulated category have been
obtained in many areas of mathematics. In this paper, as a higher-dimensional version of the …

In spite of some recent applications of ultraproducts in algebra, they remain largely unknown
to commutative algebraists, in part because they do not preserve basic properties such as …

The main goal of this paper is to prove that the idempotent completions of triangulated
categories of singularities of two schemes are equivalent if the formal completions of these …

In a recent paper, Iyama and Yoshino considered two interesting examples of isolated
singularities over which it is possible to classify the indecomposable maximal Cohen …

The Orlov spectrum is a new invariant of a triangulated category. It was introduced by D.
Orlov, building on work of A. Bondal-M. Van den Bergh and R. Rouquier. The supremum of …

Weighted projective lines, introduced by Geigle and Lenzing in 1987, are important objects
in representation theory. They have tilting bundles, whose endomorphism algebras are the …

Let (R, 𝔪) be a commutative noetherian local ring. In this paper, we prove that if 𝔪 is
decomposable, then for any finitely generated R-module M of infinite projective dimension 𝔪 …

Questions about modular representation theory of finite groups can often be reduced to
elementary abelian subgroups. This is the first book to offer a detailed study of the …

Given a two-variable invertible polynomial, we show that its category of maximally-graded
matrix factorisations is quasi-equivalent to the Fukaya-Seidel category of its Berglund-H\" …