F-injectivity and Frobenius closure of ideals in Noetherian rings of characteristic p&gt; 0

Quy, Pham Hung; Shimomoto, Kazuma

doi:10.1016/j.aim.2017.04.002

Cited by 24 publications

(27 citation statements)

References 28 publications

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“…compare with[20], Lemma 6.1). Let K be a perfect field of characteristic p > 0 and letR := K[[U, V, Y, Z]]/(U V, U Z, Z(V − Y 2 )).…”

mentioning

confidence: 85%

Frobenius Actions on Local Cohomology Modules and Deformation

Ma¹,

Quy²

2017

Nagoya Math. J.

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Abstract. Let (R, m) be a Noetherian local ring of characteristic p > 0. We introduce and study F -full and F -anti-nilpotent singularities, both are defined in terms of the Frobenius actions on the local cohomology modules of R supported at the maximal ideal. We prove that if R/(x) is F -full or F -anti-nilpotent for a nonzerodivisor x ∈ R, then so is R. We use these results to obtain new cases on the deformation of F -injectivity.

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“…compare with[20], Lemma 6.1). Let K be a perfect field of characteristic p > 0 and letR := K[[U, V, Y, Z]]/(U V, U Z, Z(V − Y 2 )).…”

mentioning

confidence: 85%

Frobenius Actions on Local Cohomology Modules and Deformation

Ma¹,

Quy²

2017

Nagoya Math. J.

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“…We note that this result is also obtained using different methods in [QS16]. <d RΓ m (R) is quasi-isomorphic to a complex of k-vector spaces.…”

Section: The Canonical Map and Thusmentioning

confidence: 63%

The dualizing complex of F-injective and Du Bois singularities

Bhatt

Schwede

2017

Math. Z.

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Abstract. Let (R, m, k) be an excellent local ring of equal characteristic. Let j be a positive integer such that H i m (R) has finite length for every 0 ≤ i < j. We prove that if R is F -injective in characteristic p > 0 or Du Bois in characteristic 0, then the truncated dualizing complex τ >−j ω q R is quasi-isomorphic to a complex of k-vector spaces. As a consequence, Finjective or Du Bois singularities with isolated non-Cohen-Macaulay locus are Buchsbaum. Moreover, when R has F -rational or rational singularities on the punctured spectrum, we obtain stronger results generalizing [Ma15] and [Ish84].

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“…[15, Proposition 3.4] for the original version when is the maximal ideal, and [1, Proposition 2.3] for the general version below). More applications can be found in [19].…”

Section: Results In Positive Characteristicmentioning

confidence: 99%

On the Associated Primes of Local Cohomology

Dao¹,

Quy²

2018

Nagoya Math. J.

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Let R be a commutative Noetherian ring of prime characteristic p. In this paper we give a short proof using filter regular sequences that the set of associated prime ideals of H t I (R) is finite for any ideal I and for any t ≥ 0 when R has finite F -representation type or finite singular locus. This extends a previous result by Takagi-Takahashi and gives affirmative answers for a problem of Huneke in many new classes of rings in positive characteristic. We also give a criterion about the singularities of R (in any characteristic) to guarantee that the set Ass H 2 I (R) is always finite.

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F-injectivity and Frobenius closure of ideals in Noetherian rings of characteristic p> 0

Abstract: Abstract. The main aim of this article is to study the relation between F -injective singularity and the Frobenius closure of parameter ideals in Noetherian rings of positive characteristic. The paper consists of the following themes, including many other topics.

Cited by 24 publications

References 28 publications

Frobenius Actions on Local Cohomology Modules and Deformation

Frobenius Actions on Local Cohomology Modules and Deformation

The dualizing complex of F-injective and Du Bois singularities

On the Associated Primes of Local Cohomology

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