NormalZ r-graded rings and normal cyclic covers

Tomari, Masataka; Watanabe, Kei-ichi

doi:10.1007/bf02567764

Cited by 20 publications

(18 citation statements)

References 7 publications

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“…The final statement is expected because, by the discussion of canonical modules for module-finite extensions in Discussion 2.2, we have that ω S ∼ = Hom R (S, ω) and [Watanabe 1991;Tomari and Watanabe 1992;Watanabe and Yoshida 2004, §3;Singh 2003] for further details and background on this technique. The result above will enable us to use this "canonical cover trick" to prove the theorem below by reduction to the quasi-Gorenstein case.…”

Section: F-purity Finite Length and Antinilpotent Modulesmentioning

confidence: 93%

The Frobenius structure of local cohomology

Enescu

Hochster

2008

ANT

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Given a local ring of positive prime characteristic there is a natural Frobenius action on its local cohomology modules with support at its maximal ideal. In this paper we study the local rings for which the local cohomology modules have only finitely many submodules invariant under the Frobenius action. In particular we prove that F-pure Gorenstein local rings as well as the face ring of a finite simplicial complex localized or completed at its homogeneous maximal ideal have this property. We also introduce the notion of an antinilpotent Frobenius action on an Artinian module over a local ring and use it to study those rings for which the lattice of submodules of the local cohomology that are invariant under Frobenius satisfies the Ascending Chain Condition.

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Section: F-purity Finite Length and Antinilpotent Modulesmentioning

confidence: 93%

The Frobenius structure of local cohomology

Enescu

Hochster

2008

ANT

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“…Since S is contained in T , this algebra is unital, and, because Hom(Hom(A⊗ S B, S), S) ∼ = Hom(Hom(B⊗ S A, S), S), it is commutative as well. This construction is similar to an algebra considered in [14].…”

Section: Class Groupsmentioning

confidence: 95%

Semidualizing modules and rings of invariants

Sanders¹

2015

J. Commut. Algebra

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“…To reduce the main theorem of this paper to Theorem 3.2, we need a variant of the cyclic covering construction, cf. [TW92] or [KM98, Section 2.4].…”

Section: Test Ideals Via Alterationsmentioning

confidence: 99%

F -singularities via alterations

Blickle¹,

Schwede²,

Tucker³

2015

ajm

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Abstract. We give characterizations of test ideals and F -rational singularities via (regular) alterations. Formally, the descriptions are analogous to standard characterizations of multiplier ideals and rational singularities in characteristic zero via log resolutions. Lastly, we establish Nadel-type vanishing theorems (up to finite maps) for test ideals, and further demonstrate how these vanishing theorems may be used to extend sections.

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NormalZ r-graded rings and normal cyclic covers

Cited by 20 publications

References 7 publications

The Frobenius structure of local cohomology

The Frobenius structure of local cohomology

Semidualizing modules and rings of invariants

F -singularities via alterations

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