Artinianness and finiteness of formal local cohomology modules with respect to a pair of ideals

Author(s)

Freitas, T. H. ^[1] ; Jorge Perez, V. H. ^[2]

Affiliation

^[1] Univ Tecnol Fed Parana, Guarapuava, PR - Brazil

^[2] Univ Sao Paulo, ICMC, Sao Carlos, SP - Brazil

• Document type: Journal article
• Source: BEITRAGE ZUR ALGEBRA UND GEOMETRIE-CONTRIBUTIONS TO ALGEBRA AND GEOMETRY; v. 58, n. 2, p. 319-340, JUN 2017.
• Web of Science Citations: 1

Abstract

Let (R, m) be a commutative Noetherian local ring, M be a finitely generated R-module and a, I and J are ideals of R. We investigate the structure of formal local cohomology modules of F-a,F-I,(i)(J) (M) and (sic)(a,I),(i)(J) (M) with respect to a pair of ideals, for all i >= 0. The main subject of the paper is to study the finiteness properties and artinianness of F-a,I,J(i) (M) and (sic)(a,m,J)(i) (M). We study the maximum and minimum integer i is an element of N such that F-a, m, J(i) (M) and (sic)(a, m, J)(i) (M) are not Artinian and we obtain some results involving cosupport, coassociated and attached primes for formal local cohomology modules with respect to a pair of ideals. Also, we give an criterion involving the concepts of finiteness and vanishing of formal local cohomology modules and Cech-formal local cohomology modules with respect to a pair of ideals. (AU)

• FAPESP's process: 13/20723-7 - Finiteness properties and Artinianness of formal local cohomology modules dened by a PAIs of ideals
• Grantee: Thiago Henrique de Freitas
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate
• FAPESP's process: 12/20304-1 - Multiplicity, mixed multiplicities, Hilbert coefficient for modules and equisingularity
• Grantee: Victor Hugo Jorge Pérez
• Support Opportunities: Scholarships abroad - Research
• FAPESP's process: 12/01084-0 - Coefficients ideals for arbitrary ideals
• Grantee: Thiago Henrique de Freitas
• Support Opportunities: Scholarships in Brazil - Doctorate