Annihilators of Local Cohomology in Characteristic Zero

Details Annihilators of Local Cohomology in Characteristic Zero Annihilators of Local Cohomology in Characteristic Zero

2006-11-07

arxiv.org/abs/math/0611169v4

Mathematics

Commutative Algebra

18 pages

Scientific paper

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.

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