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Tight Closure and Differential Simplicity

✍ Scribed by William N. Traves

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
143 KB
Volume
228
Category
Article
ISSN
0021-8693

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✦ Synopsis

The behavior of the Hasse-Schmidt algebra under Γ©tale extension is used to show that the Hasse-Schmidt algebra of a smooth algebra of finite type over a field equals the ring of differential operators. These techniques show that the formation of Hasse-Schmidt derivations does not commute with localization, providing a counterexample to a question of Brown and Kuan; their conjecture is reformulated in terms of the Hasse-Schmidt algebra. These techniques also imply that a smooth domain R is differentially simple. Tight closure is used to show that the test ideal is Hasse-Schmidt stable. Indeed, differentially simple rings of prime characteristic are strongly F-regular.

πŸ“œ SIMILAR VOLUMES

Multiplicity and Tight Closures of Param
Multiplicity and Tight Closures of Parameters
✍ Shiro Goto; Yukio Nakamura πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 104 KB

In this paper we investigate the relation between the multiplicity and the tight closure of a parameter ideals. We shall show that local rings having a parameter ideal whose multiplicity agrees with the colength of its tight closure are Cohen-Macaulay rings.

Some Results on Tight Closure and Comple
Some Results on Tight Closure and Completion
✍ S. Loepp; C. Rotthaus πŸ“‚ Article πŸ“… 2001 πŸ› Elsevier Science 🌐 English βš– 153 KB

We construct two examples of nonexcellent local Noetherian domains which demonstrate that tight closure and completion do not commute. The first example is a local normal domain A with a height one principal prime ideal P such that Λ†Ε½ . PA \* / P\*A. We also construct an example of a complete local