Cohomologia Local de Módulos Sobre Anéis Invariantes

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 auto...

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Detalles Bibliográficos
Autor: Pantoja, Pedro Henrique Oliveira
Tipo de recurso: tesis de maestría
Estado:Versión publicada
Fecha de publicación:2017
País:Brasil
Institución:Universidade Federal da Paraíba (UFPB)
Repositorio:Biblioteca Digital de Teses e Dissertações da UFPB
Idioma:portugués
OAI Identifier:oai:repositorio.ufpb.br:123456789/11236
Acceso en línea:https://repositorio.ufpb.br/jspui/handle/123456789/11236
Access Level:acceso abierto
Palabra clave:Cohomologia Local
Anéis Gorenstein
Anéis Invariantes
Local Cohomology
Gorenstein Ring
Invariant Ring
CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
Descripción
Sumario: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.