TIGHT CLOSURE IN EQUAL CHARACTERISTIC ZERO Page 1 TIGHT CLOSURE IN EQUAL
CHARACTERISTIC ZERO by Melvin Hochster and Craig Huneke Contents PREFACE …

This paper introduces a new notion of depth for complexes; it agrees with the classical
definition for modules, and coincides with earlier extensions to complexes, whenever those …

In this paper A is a commutative noetherian ring, a an ideal of A and the A-modules are
given the a-adic topology. It is a general feeling that completeness is a kind of finiteness …

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 …

Tight closure test ideals have been central to the classification of singularities in rings of
characteristic $ p> 0$, and via reduction to characteristic $ p> 0$, in equal characteristic 0 as …

Recently, in a tremendous breakthrough, R. Heitmann [11] has shown that the direct
summand conjecture holds for regular rings of dimension at most three. This was previously …

Let (R, m) be a Noetherian local ring of dimension d> 0, and let I be an mprimary ideal. One
of our goals is to study the set of I-good filtrations of R. More concretely, we will consider the …

These notes are based on five lectures given at the Summer School on Commutative
Algebra held at the CRM in Barcelona during July, 1996. I would like to thank the organizers …

We prove a uniform bound on the growth of symbolic powers of arbitrary (not necessarily
radical) ideals in arbitrary (not necessarily excellent) regular rings of all characteristics. This …

The notion of fibre product in a category is quite basic and has been studied by many
authors. Also in ring theory, it is known that the fibre product is useful in the construction of …