A dual to tight closure theory

  title={A dual to tight closure theory},
  author={Neil M. Epstein and Karl Schwede},
  journal={Nagoya Mathematical Journal},
  pages={41 - 75}
Abstract We introduce an operation on modules over an F-finite ring of characteristic p. We call this operation tight interior. While it exists more generally, in some cases this operation is equivalent to the Matlis dual of tight closure. Moreover, the interior of the ring itself is simply the big test ideal. We directly prove, without appeal to tight closure, results analogous to persistence, colon capturing, and working modulo minimal primes, and we begin to develop a theory dual to phantom… 
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