On injective resolutions of local cohomology modules

2013/12/20 by Tony J. Puthenpurakal, Puthenpurakal, Tony J. · 2 citations
Mathematics · #13H10 #Commutative Algebra (math.AC) #FOS: Mathematics #Primary 13D45 #Secondary 13D02 #math.AC #msc:13D02 #msc:13D45 #msc:13H10

paper · pdf · doi:10.48550/arxiv.1312.5852

arxiv created 2013/12/20 · arxiv updated 2013/12/23

Abstract

Let K be a field of characteristic zero and let R = K[X₁,…,X_n]. Let I be an ideal in R and let M = Hⁱ_I(R) be the i^th-local cohomology module of R with respect to I. Let c = injdim M. We prove that if P is a prime ideal in R with Bass number μ_c(P,M) > 0 then P is a maximal ideal in R.

Cited by

• Local cohomology modules of a regular affine domain
• Bounds on Bass numbers of local cohomology modules

Related

• Local cohomology with support in ideals of maximal minors
• A Note on the injective dimension of local cohomology modules
• Bass Numbers of the First Nonzero Local Cohomology Module
• Finiteness properties of duals of local cohomology modules
• Cofiniteness of generalized local cohomology modules