Tight closure

Winfried Bruns

Bull. Amer. Math. Soc. 33 (1996), pp. 447-457 

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 methods in commutative 
algebra'. It ties several strands of commutative algebra and algebraic
geometry together: invariant theory, rational singularities, the 
Brian\,con--Skoda theorem, the `homological conjectures', big Cohen--Macaulay 
modules and algebras, and various other topics.