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Centers of F-purity

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Abstract

In this paper, we study a positive characteristic analogue of the centers of log canonicity of a pair (R, Δ). 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 Δ = 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 Lyubeznik and Smith.

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  1. Department of Mathematics, University of Michigan, East Hall, 530 Church Street, Ann Arbor, MI, 48109, USA

    Karl Schwede

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  1. Karl Schwede
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Correspondence to Karl Schwede.

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K. Schwede was partially supported by a National Science Foundation postdoctoral fellowship and by RTG grant number 0502170.

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Schwede, K. Centers of F-purity. Math. Z. 265, 687–714 (2010). https://doi.org/10.1007/s00209-009-0536-5

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