Tight closure

Abstract

The theory of tight closure was created by Mel Hochster and Craig Huneke about ten years ago. Assisted by numerous contributions of others, they have continuously developed the theory since then. ‘Tight closure’ can now be regarded as a synonym for ‘characteristic p p methods in commutative algebra’. It ties several strands of commutative algebra and algebraic geometry together: invariant theory, rational singularities, the Briançon–Skoda theorem, the ‘homological conjectures’, big Cohen–Macaulay modules and algebras, and various other topics.