The associated graded module of the test module filtration

Stäbler, Axel

doi:10.1080/00927872.2021.1882475

Cited by 2 publications

(1 citation statement)

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“…Let us now give a brief summary of the contents of this paper. In Section 1 we explain the notion of non-F -pure ideal and recall several technical results from [Stä17] that we shall need. In Section 2 we recall the notion on maximal non-lc ideals, and prove the above theorem after some preliminary work.…”

Section: Introductionmentioning

confidence: 99%

Reductions of non-lc ideals and non F-pure ideals assuming weak ordinarity

Stäbler

2020

manuscripta math.

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Assume X is a variety over C, A ⊆ C is a finitely generated Zalgebra and X A a model of X (i.e. X A × A C ∼ = X). Assuming the weak ordinarity conjecture we show that there is a dense set S ⊆ Spec A such that for every closed point s of S the reduction of the maximal non-lc ideal filtration J (X, ∆, a λ ) coincides with the non-F -pure ideal filtration σ(Xs, ∆s, a λ s ) provided that (X, ∆) is klt or if (X, ∆) is log canonical, a is locally principal and the non-klt locus is contained in a.

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Section: Introductionmentioning

confidence: 99%

Reductions of non-lc ideals and non F-pure ideals assuming weak ordinarity

Stäbler

2020

manuscripta math.

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Bernstein-Sato theory for singular rings in positive characteristic

Jeffries

Núñez-Betancourt²,

Quinlan-Gallego

2023

Trans. Amer. Math. Soc.

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The Bernstein-Sato polynomial is an important invariant of an element or an ideal in a polynomial ring or power series ring of characteristic zero, with interesting connections to various algebraic and topological aspects of the singularities of the vanishing locus. Work of Mustaţă, later extended by Bitoun and the third author, provides an analogous Bernstein-Sato theory for regular rings of positive characteristic. In this paper, we extend this theory to singular ambient rings in positive characteristic. We establish finiteness and rationality results for Bernstein-Sato roots for large classes of singular rings, and relate these roots to other classes of numerical invariants defined via the Frobenius map. We also obtain a number of new results and simplified arguments in the regular case.

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The associated graded module of the test module filtration

Cited by 2 publications

References 22 publications

Reductions of non-lc ideals and non F-pure ideals assuming weak ordinarity

Reductions of non-lc ideals and non F-pure ideals assuming weak ordinarity

Bernstein-Sato theory for singular rings in positive characteristic

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