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Doctoral Thesis
DOI
10.11606/T.55.2017.tde-13012017-083727
Document
Author
Full name
Carlos Henrique Tognon
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2016
Supervisor
Committee
Pérez, Victor Hugo Jorge (President)
Carvalho, Cícero Fernandes de
Miranda Neto, Cleto Brasileiro
Okamoto, Bruna Oréfice
Saia, Marcelo José
Title in Portuguese
Propriedades da homologia local com respeito a um par de ideais e limite inverso de homologia local
Keywords in Portuguese
Cohomologia local
Homologia local
Limite inverso.
Abstract in Portuguese
Neste trabalho, introduzimos uma generalização da noção de módulo de homologia local de um módulo com respeito a um ideal, o qual nós chamamos de módulo de homologia local com respeito a um par de ideais. Estudamos suas várias propriedades tais como teoremas de anulamento e de não anulamento, e Artinianidade. Também fazemos sua conexão com a homologia e cohomologia local usual. Introduzimos uma generalização da noção de largura de um ideal sobre um módulo aplicando o conceito de módulo de homologia local com respeito a um par de ideais. Também introduzimos o conceito de um módulo co-Cohen-Macaulay para um par de ideais, o qual é uma generalização o conceito de um módulo co-Cohen-Macaulay. Para finalizar, introduzimos o limite inverso de homologia local, e estudamos algumas de suas propriedades, analisamos a sua estrutura, o anulamento, não anulamento e Artinianidade.
Title in English
Properties of local homology with respect to a pair of ideals and inverse limit of local homology
Keywords in English
Inverse limit.
Local cohomology
Local homology
Abstract in English
In this work, we introduce a generalization of the notion of local homology module of a module with respect to an ideal, which we call of local homology module with respect to a pair of ideals. We study its various properties such as vanishing and nonvanishing theorems, and Artinianness. We also do its connection with ordinary local homology and cohomology. We introduce a generalization of the notion of width of an ideal on a module applying the concept of local homology module with respect to a pair of ideals. Also we introduce the concept of a co-Cohen-Macaulay module for a pair of ideals, what is a generalization of the concept of a co-Cohen-Macaulay module. To finish, we introduce the inverse limit of local homology, and we study some of its properties, we analyze the their structure, the vanishing, non-vanishing and Artinianness.
 
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Publishing Date
2017-01-13
 
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