Výsledky vyhledávání - "Dietz, Geoffrey D."

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Big Cohen-Macaulay and seed algebras in equal characteristic zero via ultraproducts

Autor: Dietz, Geoffrey D., G, Rebecca R.

Let $R$ be a commutative, local, Noetherian ring. In a past article, the first author developed a theory of $R$-algebras, termed seeds, that can be mapped to balanced big Cohen-Macaulay $R$-algebras. In prime characteristic $p$, seeds can be characte

Externí odkaz: http://arxiv.org/abs/1608.08193

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Axiomatic Closure Operations, Phantom Extensions, and Solidity

Autor: Dietz, Geoffrey D.

In this article, we generalize a previously defined set of axioms for a closure operation that induces balanced big Cohen-Macaulay modules. While the original axioms were only defined in terms of finitely generated modules, these new ones will apply

Externí odkaz: http://arxiv.org/abs/1511.04286

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A Characterization of Closure Operations That Induce Big Cohen-Macaulay Modules

Autor: Dietz, Geoffrey D.

Publikováno v: Proc. of the Amer. Math. Soc., 138 (2010), No. 11, 3849--3862

The intent of this paper is to present a set of axioms that are sufficient for a closure operation to generate a balanced big Cohen-Macaulay module B over a complete local domain R. Conversely, we show that if such a B exists over R, then there exist

Externí odkaz: http://arxiv.org/abs/0911.0398

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Big Cohen-Macaulay Algebras and Seeds

Autor: Dietz, Geoffrey D.

Publikováno v: Trans. of the Amer. Math. Soc., 359 (2007), No. 12, 5959--5989

We delve into the properties possessed by algebras, which we have termed seeds, that map to big Cohen-Macaulay algebras. We will show that over a complete local domain of positive characteristic any two big Cohen-Macaulay algebras map to a common big

Externí odkaz: http://arxiv.org/abs/math/0508358

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Tight Closure of Finite Length Modules in Graded Rings

Autor: Dietz, Geoffrey D.

Publikováno v: Journal of Algebra, 306 (2006), No. 2, 520--534

We look at how the equivalence of tight closure and plus closure (or Frobenius closure) in the homogeneous m-coprimary case implies the same closure equivalence in the non-homogeneous m-coprimary case in standard graded rings. Although our result doe

Externí odkaz: http://arxiv.org/abs/math/0508357

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