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 …

A ring has bounded factorizations if every cancellative nonunit a∈ R can be written as a
product of atoms and there is a bound λ (a) on the lengths of such factorizations. The …

We continue investigating the interaction between flatness and a a-adic completion for
infinitely generated A-modules. Here A is a commutative ring and aa is a finitely generated …

We begin by recalling the role that weak proregularity of an ideal in a commutative ring has
in derived completion and adic flatness. We also introduce the new concepts of idealistic …

We survey the basic theory of non-commutative K3 surfaces, with a particular emphasis to
the ones arising from cubic fourfolds. We focus on the problem of constructing Bridgeland …

The main result of the present paper concerns finiteness properties of Floer theoretic
invariants on affine log Calabi-Yau varieties $ X $. Namely, we show that:(a) the degree zero …

In this paper, we introduce the class of Cohen-Macaulay (= CM) dg (= differential graded)
modules over Gorenstein dg algebras and study their basic properties. We show that the …

We study the transfer of (co) silting objects in derived categories of module categories via
the extension functors induced by a morphism of commutative rings. It is proved that the …

Let A be an associative non-positive differential graded ring. In this paper we make a
detailed study of a category Inj (A) of left DG-modules over A which generalizes the category …

By extending some basic results of Grothendieck and Foxby about local cohomology to
commutative DG-rings, we prove new amplitude inequalities about finite DG-modules of …