Geometric Interpretation of Tight Closure and Test Ideals

  title={Geometric Interpretation of Tight Closure and Test Ideals},
  author={Nobuo Hara},
We study tight closure and test ideals in rings of characteristic p 0 using resolution of singularities. The notions of F -rational and F regular rings are defined via tight closure, and they are known to correspond with rational and log terminal singularities, respectively. In this paper, we reformulate this correspondence by means of the notion of the test ideal, and generalize it to wider classes of singularities. The test ideal is the annihilator of the tight closure relations and plays a… CONTINUE READING
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