On the endomorphism ring and Cohen-Macaulayness of local cohomology defined by a pair of ideals

Autor(es)

Freitas, Thiago H. ^[1] ; Jorge Perez, Victor H. ^[2]

Afiliação do(s) autor(es)

^[1] Univ Tecnol Fed Parana, Campus Guarapuava, BR-85053525 Guarapuava - Brazil

^[2] Univ Sao Paulo, ICMC, Caixa Postal 668, BR-13560970 Sao Carlos, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: CZECHOSLOVAK MATHEMATICAL JOURNAL; v. 69, n. 2, p. 453-470, JUN 2019.
• Citações Web of Science: 0

Resumo

Let a, I, J be ideals of a Noetherian local ring (R,m,k). Let M and N be finitely generated R-modules. We give a generalized version of the Duality Theorem for Cohen-Macaulay rings using local cohomology defined by a pair of ideals. We study the behavior of the endomorphism rings of HI,Jt(M) and HI,Jt(M)), where t is the smallest integer such that the local cohomology with respect to a pair of ideals is nonzero and D(-):= Hom(R)(-, E-r(k)) is the Matlis dual functor. We show that if R is a d-dimensional complete Cohen-Macaulay ring and HI,Ji(R) = 0 for all i t, the natural homomorphism R Hom(r)(HI,Jt(K-R),HI,Jt(K-R)) is an isomorphism, where K-R denotes the canonical module of R. Also, we discuss the depth and Cohen-Macaulayness of the Matlis dual of the top local cohomology modules with respect to a pair of ideals. (AU)

• Processo FAPESP: 13/20723-7 - Propriedades de finitude e Artinianissidade do módulo cohomologia local formal, definida por um par de ideais
• Beneficiário: Thiago Henrique de Freitas
• Linha de fomento: Bolsas no Exterior - Estágio de Pesquisa - Doutorado
• Processo FAPESP: 12/01084-0 - Ideais coeficientes para ideais arbitrários
• Beneficiário: Thiago Henrique de Freitas
• Linha de fomento: Bolsas no Brasil - Doutorado