Centers of F-purity

2008/07/31 by Karl Schwede · 1 citation
Mathematics · #math.AC #math.AG #msc:13A35 #msc:14B05

paper · pdf · doi:10.1007/s00209-009-0536-5

published as Math. Z. Vol. 265, No 3, 687-714, 2010 · Typos corrected. To appear in Math. Z

arxiv created 2009/05/04 · arxiv updated 2010/05/17

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 F(E_R(k))-submodules of E_R(k) as defined by Smith and Lyubeznik.

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