Annihilators of Local Cohomology in Characteristic Zero

2006/11/07 by Paul Roberts, Anurag K. Singh, Roberts, Paul +3
Mathematics · #13D22 #13D45 #14K05 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #math.AC #math.AG #msc:13D22 #msc:13D45 #msc:14K05

paper · pdf · doi:10.48550/arxiv.math/0611169

18 pages

openalex publication_date 2006/11/07 · arxiv created 2007/08/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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