p-torsion elements in local cohomology modules
By Anurag Singh. 2004
128 citations recorded by the source corpus.
For every prime integer p, M. Hochster conjecturedthe existence of certain p-torsion elements in a local cohomology module over a regular ring of mixedcharacteristic. We show that Hochster's conjecture is false. We next con- struct an example where a local cohomology module over a hypersurface has p- torsion elements for every prime integer p, andconsequently has infinitely many associatedprime ideals. For a commutative Noetherian ring R and an ideal a ⊂ R, the finiteness properties of the local cohomology modules H i
Subfields: Algebra and Number Theory, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/1fa481474f319222968f10934bd17b64bd5545b3
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In Algebra and Number Theory
- M. Dibaei
- Siamak Yassemi
- Le Thanh Nhan
- K. Divaani-Aazar
- A. Mafi
- Irena Swanson
- Anurag Singh
- Cameron Wickham
In Geometry and Topology
- M. Dibaei
- Siamak Yassemi
- Le Thanh Nhan
- K. Divaani-Aazar
- A. Mafi
- Irena Swanson
- Anurag Singh
- Cameron Wickham
Citations in the corpus
- Associated primes of local cohomology modules and of Frobenius powers (2004, background): “. Introduction Let R be a commutative Noetherian ring and a ⊂ R an ideal. In [Hu1] Huneke asked whether the number of associated prime ideals of a local cohomology module Hn a (R) is always finite. In [Si] the first author constructed an example of a hypersurface R = Z[u,v,w,x,y,z]/(ux+vy +wz) for whi”
- ON GENERALIZED REGULAR SEQUENCES AND THE FINITENESS FOR ASSOCIATED PRIMES OF LOCAL COHOMOLOGY MODULES (2005, background): “Recently, Singh (2000) (in the nonlocal case) and Katzman (2002) (in the local case) have given examples to show that AssHiI M is generally not a finite set.”
- Associated primes of local cohomology modules (2004, background): “In this regard, the best known result is that for a finitely generated R-module M if either a is principal or R is local and dimR/a = 1, then the modules H i a (M) are a-cofinite.”
- Cofiniteness of local cohomology modules for ideals of small dimension (2009, unknown): “Katzman), see [32] (resp.”
- Associated primes and cofiniteness of local cohomology modules (2004, methodology): “0 −→ R/p b −→ R/p → R/(p + bR) → 0 204 M.T. Dibaei, S . Yassemi”