Centers of F-purity

Abstract

In this paper, we study a positive characteristic analogue of the centers of log canonicity of a pair $(R,\Delta )$. We call these analogues centers of $F$-purity. We prove positive characteristic analogues of subadjunction-like results, prove new stronger subadjunction-like results, and in some cases, lift these new results to characteristic zero. Using a generalization of centers of $F$-purity which we call uniformly $F$-compatible ideals, we give a characterization of the test ideal (which unifies several previous characterizations). Finally, in the case that $\Delta =0$, we show that uniformly $F$-compatible ideals coincide with the annihilators of the $\mathcal{F}(E_R(k))$-submodules of $E_R(k)$ as defined by Smith and Lyubeznik.

Typos corrected. To appear in Math. Z

References in corpus (1)

• Singularities on normal varieties

Cited by in corpus (19)

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• On Strongly $F$-Regular Inversion of Adjunction
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• The gamma construction and asymptotic invariants of line bundles over arbitrary fields
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• On the behavior of singularities at the $F$-pure threshold
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• Tate algebras and Frobenius non-splitting of excellent regular rings
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• Tame fundamental groups of pure pairs and Abhyankar's lemma
• Centers of perfectoid purity
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• Uniform approximation of Abhyankar valuation ideals in function field of prime characteristic