Illinois Journal of Mathematics

Annihilators of local cohomology in characteristic zero

Paul Roberts, Anurag K. Singh, and V. Srinivas

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This paper discusses the problem of whether it is possible to annihilate elements of local cohomology modules by elements of arbitrarily small order under a fixed valuation. We first discuss the general problem and its relationship to the Direct Summand Conjecture, and next present two concrete examples where annihilators with small order are shown to exist. We then prove a more general theorem, where the existence of such annihilators is established in some cases using results on abelian varieties and the Albanese map.

Article information

Illinois J. Math., Volume 51, Number 1 (2007), 237-254.

First available in Project Euclid: 20 November 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 13D22: Homological conjectures (intersection theorems)
Secondary: 13D45: Local cohomology [See also 14B15] 14K05: Algebraic theory


Roberts, Paul; Singh, Anurag K.; Srinivas, V. Annihilators of local cohomology in characteristic zero. Illinois J. Math. 51 (2007), no. 1, 237--254. doi:10.1215/ijm/1258735334.

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