An application of generalized Matlis duality for quasi-\F-modules to the Artinianness of local cohomology modules

2011/06/14 by Danny Tobisch, Tobisch, Danny
Mathematics · #13D45 (Secondary) #13H05 (Primary) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #msc:13D45 #msc:13H05

paper · pdf · doi:10.48550/arxiv.1106.2639

10 pages

arxiv created 2011/06/14 · arxiv updated 2011/06/15

Abstract

We use a result of Hellus about generalized local duality to describe some generalized Matlis duals for certain quasi-\F-modules. Furthermore, we apply this description to obtain examples for non-artinian local cohomology modules by the theory of \F-modules. In particular, we get a new view on Hartshorne's counterexample for a conjecture by Grothendieck about the finiteness of Hom_R(R/I,Hⁱ_I(R)) for a noetherian local Ring R and an ideal I ⊆ R.

Related

• Some results on local cohomology modules
• Finiteness properties of duals of local cohomology modules
• Some results on generalized local cohomology modules
• On Artinianness of Formal Local Cohomology
• Artinianness of local cohomology modules