Tight Closure in Equal Characteristic

  title={Tight Closure in Equal Characteristic},
  author={Melvin Hochster},
  • Melvin Hochster
  • Published 2014
We rst discuss joint work of Craig Huneke and the author, giving an overview of the status of tight closure theory both in characteristic p and in equal characteristic 0, including recently discovered interconnections with the existence of big Cohen-Macaulay algebras, especially their existence in a weakly functorial sense. For example, either tight closure or the functorial existence of big Cohen-Macaulay algebras can be used to prove that direct summands of regular rings are Cohen-Macaulay in… CONTINUE READING

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