Algorithms for graded injective resolutions and local cohomology over semigroup rings
Publication
, Journal Article
Helm, D; Miller, E
Published in: Journal of Symbolic Computation
March 1, 2005
Let Q be an affine semigroup generating ℤd, and fix a finitely generated ℤd-graded module M over the semigroup algebra k[Q] for a field k. We provide an algorithm to compute a minimal ℤd-graded injective resolution of M up to any desired cohomological degree. As an application, we derive an algorithm computing the local cohomology modules HIi supported on any monomial (that is, ℤd-graded) ideal I. Since these local cohomology modules are neither finitely generated nor finitely cogenerated, part of this task is defining a finite data structure to encode them. © 2005 Elsevier Ltd. All rights reserved.
Duke Scholars
Published In
Journal of Symbolic Computation
DOI
ISSN
0747-7171
Publication Date
March 1, 2005
Volume
39
Issue
3-4 SPEC. ISS.
Start / End Page
373 / 395
Related Subject Headings
- General Mathematics
- 4903 Numerical and computational mathematics
- 4901 Applied mathematics
- 0802 Computation Theory and Mathematics
- 0103 Numerical and Computational Mathematics
- 0102 Applied Mathematics
Citation
APA
Chicago
ICMJE
MLA
NLM
Helm, D., & Miller, E. (2005). Algorithms for graded injective resolutions and local cohomology over semigroup rings. Journal of Symbolic Computation, 39(3-4 SPEC. ISS.), 373–395. https://doi.org/10.1016/j.jsc.2004.11.009
Helm, D., and E. Miller. “Algorithms for graded injective resolutions and local cohomology over semigroup rings.” Journal of Symbolic Computation 39, no. 3-4 SPEC. ISS. (March 1, 2005): 373–95. https://doi.org/10.1016/j.jsc.2004.11.009.
Helm D, Miller E. Algorithms for graded injective resolutions and local cohomology over semigroup rings. Journal of Symbolic Computation. 2005 Mar 1;39(3-4 SPEC. ISS.):373–95.
Helm, D., and E. Miller. “Algorithms for graded injective resolutions and local cohomology over semigroup rings.” Journal of Symbolic Computation, vol. 39, no. 3-4 SPEC. ISS., Mar. 2005, pp. 373–95. Scopus, doi:10.1016/j.jsc.2004.11.009.
Helm D, Miller E. Algorithms for graded injective resolutions and local cohomology over semigroup rings. Journal of Symbolic Computation. 2005 Mar 1;39(3-4 SPEC. ISS.):373–395.
Published In
Journal of Symbolic Computation
DOI
ISSN
0747-7171
Publication Date
March 1, 2005
Volume
39
Issue
3-4 SPEC. ISS.
Start / End Page
373 / 395
Related Subject Headings
- General Mathematics
- 4903 Numerical and computational mathematics
- 4901 Applied mathematics
- 0802 Computation Theory and Mathematics
- 0103 Numerical and Computational Mathematics
- 0102 Applied Mathematics