A dual to tight closure theory
نویسندگان
چکیده
منابع مشابه
An introduction to tight closure
This is an expanded version of my lecture at the Conference in Commutative Algebra and Algebraic Geometry in Messina Italy in June 1999. The purpose of the talk was to give a brief introduction to the subject of tight closure, aimed at commutative algebraists who have not before studied this topic. The first part focused mainly on the definition and basic properties, with the second part focusi...
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Tight 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 کاملTight Closure in Graded Rings
This paper facilitates the computation of tight closure by giving giving upper and lower bounds on the degrees of elements that need to be checked for inclusion in the tight closure of certain homogeneous ideals in a graded ring. Differential operators are introduced to the study of tight closure, and used to prove that the degree of any element in the tight closure of a homogeneous ideal (but ...
متن کاملTight Closure and Projective Bundles
We formulate problems of tight closure theory in terms of projective bundles and subbundles. This provides a geometric interpretation of such problems and allows us to apply intersection theory to them. This yields new results concerning the tight closure of a primary ideal in a two-dimensional graded domain.
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ژورنال
عنوان ژورنال: Nagoya Mathematical Journal
سال: 2014
ISSN: 0027-7630,2152-6842
DOI: 10.1215/00277630-2376749