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Tight Closure in Characteristic Zero. Local Case

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1999)

Abstract

The goal of this chapter is to extend the tight closure theory from the previous chapter to include all Noetherian rings containing a field. However, the theory becomes more involved, especially if one wants to maintain full functoriality. We opt in these notes to forego this cumbersome route (directing the interested reader to the joint paper [6] with Aschenbrenner), and only develop the theory minimally as to still obtain the desired applications. In particular, we will only focus on the local case.

Keywords

  • Prime Ideal
  • Local Ring
  • Characteristic Zero
  • Homomorphic Image
  • Noetherian Ring

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References

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Correspondence to Hans Schoutens .

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Schoutens, H. (2010). Tight Closure in Characteristic Zero. Local Case. In: The Use of Ultraproducts in Commutative Algebra. Lecture Notes in Mathematics(), vol 1999. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13368-8_7

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