Test ideals in non- -Gorenstein rings

Author:
Karl Schwede

Journal:
Trans. Amer. Math. Soc. **363** (2011), 5925-5941

MSC (2010):
Primary 13A35, 14F18, 14B05

Published electronically:
June 3, 2011

MathSciNet review:
2817415

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Abstract | References | Similar Articles | Additional Information

Abstract: Suppose that is an -finite normal variety in characteristic . In this paper we show that the big test ideal is equal to , where the sum is over such that is -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 is not even necessarily normal.

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Additional Information

**Karl Schwede**

Affiliation:
Department of Mathematics, The Pennsylvania State University, 318C McAllister Building, University Park, Pennsylvania 16802

Email:
schwede@math.psu.edu

DOI:
https://doi.org/10.1090/S0002-9947-2011-05297-9

Keywords:
Tight closure,
test ideal,
$\mathbb{Q}$-Gorenstein,
log $\mathbb{Q}$-Gorenstein,
multiplier ideal,
$F$-singularities

Received by editor(s):
June 24, 2009

Received by editor(s) in revised form:
November 30, 2009

Published electronically:
June 3, 2011

Additional Notes:
The author was partially supported by a National Science Foundation postdoctoral fellowship and by RTG grant number 0502170.

Article copyright:
© Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.