scholarly journals Parameter-test-ideals of Cohen–Macaulay rings

2008 ◽  
Vol 144 (4) ◽  
pp. 933-948 ◽  
Author(s):  
Mordechai Katzman
Keyword(s):  
Local Cohomology ◽  
Residue Field ◽  
Injective Hull ◽  
Local Cohomology Modules ◽  
D Modules ◽  
Frobenius Map ◽  
Parameter Test ◽  
Computing Parameter ◽  
Injective Hulls ◽  
Cohomology Modules

AbstractWe describe an algorithm for computing parameter-test-ideals in certain local Cohen–Macaulay rings. The algorithm is based on the study of a Frobenius map on the injective hull of the residue field of the ring and on the application of Sharp’s notion of ‘special ideals’. Our techniques also provide an algorithm for computing indices of nilpotency of Frobenius actions on top local cohomology modules of the ring and on the injective hull of its residue field. The study of nilpotent elements on injective hulls of residue fields also yields a great simplification of the proof of the celebrated result in the article Generators of D-modules in positive characteristic (J. Alvarez-Montaner, M. Blickle and G. Lyubeznik, Math. Res. Lett. 12 (2005), 459–473).

scholarly journals The Frobenius action on local cohomology modules in mixed characteristic

2007 ◽  
Vol 143 (6) ◽  
pp. 1478-1492 ◽  
Author(s):  
Kazuma Shimomoto
Keyword(s):  
Local Cohomology ◽  
Ring Theory ◽  
Local Rings ◽  
New Approach ◽  
Mixed Characteristic ◽  
Local Cohomology Modules ◽  
Frobenius Map ◽  
The Subject ◽  
Torsion Modules ◽  
Cohomology Modules

AbstractHeitmann’s proof of the direct summand conjecture has opened a new approach to the study of homological conjectures in mixed characteristic. Inspired by his work and by the methods of almost ring theory, we discuss a normalized length for certain torsion modules, which was introduced by Faltings. Using the normalized length and the Frobenius map, we prove some results of local cohomology for local rings in mixed characteristic, which has an immediate implication for the subject of splinters studied by Singh.

Cofiniteness and vanishing of local cohomology modules

1991 ◽  
Vol 110 (3) ◽  
pp. 421-429 ◽  
Author(s):  
Craig Huneke ◽  
Jee Koh
Keyword(s):  
Local Ring ◽  
Maximal Ideal ◽  
Local Cohomology ◽  
Residue Field ◽  
Finitely Generated ◽  
Noetherian Local Ring ◽  
Local Cohomology Modules ◽  
Cohomology Modules

Let R be a noetherian local ring with maximal ideal m and residue field k. If M is a finitely generated R-module then the local cohomology modules are known to be Artinian. Grothendieck [3], exposé 13, 1·2 made the following conjecture:If I is an ideal of R and M is a finitely generated R-module, then HomR (R/I, ) is finitely generated.

scholarly journals Artinianness of local cohomology modules

2014 ◽  
Vol 52 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Moharram Aghapournahr ◽  
Leif Melkersson
Keyword(s):  
Local Cohomology ◽  
Local Cohomology Modules ◽  
Cohomology Modules

On the associated primes of local cohomology modules

1999 ◽  
Vol 27 (12) ◽  
pp. 6191-6198 ◽  
Author(s):  
K. Khashyarmanesh ◽  
Sh Salarian
Keyword(s):  
Local Cohomology ◽  
Associated Primes ◽  
Local Cohomology Modules ◽  
Cohomology Modules

Some properties of local homology and local cohomology modules

2013 ◽  
Vol 50 (1) ◽  
pp. 129-141
Author(s):  
Tran Nam
Keyword(s):  
Local Cohomology ◽  
Local Homology ◽  
Local Cohomology Modules ◽  
Cohomology Modules ◽  
Compact Module

We study some properties of representable or I-stable local homology modules HiI (M) where M is a linearly compact module. By duality, we get some properties of good or at local cohomology modules HIi (M) of A. Grothendieck.

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