Tight Closure Does Not Commute with Localization
نویسنده
چکیده
We give an example showing that tight closure does not commute with localization. Mathematical Subject Classification (2000): 13A35, 14H60
منابع مشابه
Localization and Test Exponents for Tight Closure
We introduce the notion of a test exponent for tight closure, and explore its relationship with the problem of showing that tight closure commutes with localization, a longstanding open question. Roughly speaking, test exponents exist if and only if tight closure commutes with localization: mild conditions on the ring are needed to prove this. We give other, independent, conditions that are nec...
متن کاملTight Closure and Differential Simplicity
The behavior of the Hasse–Schmidt algebra under étale 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 reformula...
متن کاملThe single Drosophila ZO-1 protein Polychaetoid regulates embryonic morphogenesis in coordination with Canoe/afadin and Enabled
Adherens and tight junctions play key roles in assembling epithelia and maintaining barriers. In cell culture zonula occludens (ZO)-family proteins are important for assembly/maturation of both tight and adherens junctions (AJs). Genetic studies suggest that ZO proteins are important during normal development, but interpretation of mouse and fly studies is limited by genetic redundancy and/or a...
متن کاملF-regularity relative to modules
In this paper we will generalize some of known results on the tight closure of an ideal to the tight closure of an ideal relative to a module .
متن کاملForcing Algebras, Syzygy Bundles, and Tight Closure
We give a survey about some recent work on tight closure and Hilbert-Kunz theory from the viewpoint of vector bundles. This work is based in understanding tight closure in terms of forcing algebras and the cohomological dimension of torsors of syzygy bundles. These geometric methods allowed to answer some fundamental questions of tight closure, in particular the equality between tight closure a...
متن کامل