Tight Closure, Invariant Theory, and the Briancon-Skoda Theorem Page 1 JOURNAL OF
THE AMERICAN MATHEMATICAL SOCIETY Volume 3, Number 1, January 1990 TIGHT …

But, in the further development of a branch of mathematics, the human mind, encouraged by
the success of its solutions, becomes conscious of its independence. It evolves from itself …

This paper deals with tight closure theory in positive characteristic. After a good deal of
preliminary work in the first five sections, including a treatment of F-rationality and a …

This book is aimed to provide an introduction to local cohomology which takes cognizance
of the breadth of its interactions with other areas of mathematics. It covers topics such as the …

Abstract We establish the Minimal Model Program for arithmetic threefolds whose residue
characteristics are greater than five. In doing this, we generalize the theory of global F …

Let $ R $ be a commutative Noetherian ring. We study $ R $–modules, and complexes of
such, with excellent duality properties. While their common properties are strong enough to …

Let R be a hypersurface domain, that is, a ring of the form S/(f), where S is a regular local
ring and f is a prime element. Suppose M and N are finitely generated R-modules. We prove …

This book gives a detailed account of recent work on relations between commutative
algebra and intersection theory, with a particular emphasis on applications of the theory of …

This book presents an account of several conjectures arising in commutative algebra from
the pioneering work of Serre and Auslander-Buchsbaum. The approach is via Hochster's' …

A characterization is given of those Noetherian rings $ R $ such that whenever $ R $ is
ideally closed ($\equiv $ cyclically pure) in an extension algebra $ S $, then $ R $ is pure in …