Test ideals in non-Q-Gorenstein rings

2009/06/30 by Karl Schwede · 1 citation
Mathematics · #math.AC #math.AG #msc:13A35 #msc:14B05

paper · pdf

published as Trans. Amer. Math. Soc. 363 (2011), no. 11, 5925--5941 · 18 pages, minor changes, to appear in Transactions of the American Mathematical Society

arxiv created 2010/01/26 · arxiv updated 2011/07/26

Abstract

Suppose that X = \Spec R is an F-finite normal variety in characteristic p > 0. In this paper we show that the big test ideal τ_b(R) = \tld τ(R) is equal to ∑_Δ τ(R; Δ) where the sum is over Δ such that K_X + Δ is \bQ-Cartier. This affirmatively answers a question asked by various people, including Blickle, Lazarsfeld, K. Lee and K. Smith. Furthermore, we have a version of this result in the case that R is not even necessarily normal.

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