Illinois Journal of Mathematics

Annihilators of local cohomology in characteristic zero

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

Full-text: Open access

Abstract

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

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

Dates
First available in Project Euclid: 20 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258735334

Digital Object Identifier
doi:10.1215/ijm/1258735334

Mathematical Reviews number (MathSciNet)
MR2346196

Zentralblatt MATH identifier
1127.13013

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

Citation

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. https://projecteuclid.org/euclid.ijm/1258735334


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