Cohomologia Local de Módulos Sobre Anéis Invariantes

• Ano de defesa: 2017
• Autor(a) principal: Pantoja, Pedro Henrique Oliveira
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal da Paraíba; Brasil; Matemática; Programa de Pós-Graduação em Matemática; UFPB
• Palavras-chave em Português: Cohomologia Local; Anéis Gorenstein; Anéis Invariantes; Local Cohomology; Gorenstein Ring; Invariant Ring; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: https://repositorio.ufpb.br/jspui/handle/123456789/11236

In this work we study local cohomology of modules on invariant rings inspired by the results of Sharp, Huneke and Lyubeznik. In fact the main result was demonstrated by Tony J. Puthenpurakal: Let K be a field and let R be a regular domain containing K. Let G be a finite subgroup of the group of automorphisms of R. We assume that |G| is invertible in K. Let Rtt be the ring of invariants of G. Let I be an ideal in Rtt. Fix i ≥ 0, if Rtt is Gorenstein then: (I) injdimRG HI (Rtt) ≤ dimsupp Hi(Rtt); (II) Hj (Hi(Rtt)) is injective, where m is any maximal ideal of Rtt; m I (III) µj(P, Hi(Rtt)) = µj(P j, Hi (R)) where P j is any prime in R lying above. I IR We also prove that if P is a prime ideal in Rtt with Rtt not Gorenstein then either the Bass number µj(P, Hi(Rtt))is zero for all j or there exists c such that µj(P, Hi(Rtt)) = 0 I I for j < c and µj(P, Hi(Rtt)) > 0 for all j ≥ c.