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Master's Dissertation
DOI
10.11606/D.55.2019.tde-22032019-163616
Document
Author
Full name
Piere Alexander Rodriguez Valerio
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2018
Supervisor
Committee
Mirzaii, Behrooz (President)
Manzoli Neto, Oziride
Ruffino, Fabio Ferrari
Salehyan, Parham
Title in Portuguese
Regulador de Borel na K-teoria algébrica
Keywords in Portuguese
Anel de inteiros
K-grupos
K-teoria algebraíca
Mapa regulador de Borel
Abstract in Portuguese
Neste trabalho,nos apresentamos a K-teoria algébrica a qual é um ramo da álgebra que associa para cada anel comutativo comunidade R, uma sequencia de grupos abelianos ditos de n-ésimos K-grupos do anel R, denotada por Kn(R) . A meados da década de 1950,Alexander Grothendieck da a definição do K0(R) de um anel R. Em 1962, Hyman Bass e Stephen Schanuel apresenta a primeira definição adequada do K1(R) de um anel R. Em 1970, Daniel Quillen da uma definição geral dos K-grupos de um anel R a partir da +- construção do espaço classificante BGL(R). Nosso interesse é o estudo dos K-grupos sobre o anel de inteiros OF sobre um corpo numérico F. Usando alguns resultados de homologia dos grupos lineares, neste trabalho daremos a definição do mapa regulador de Borel.
Title in English
Borel regulator in algebraic k-theory
Keywords in English
Algebraic k-theory
Borel's regulator
K-groups
Ring of integers
Abstract in English
In this paper,we present the algebraic K-theory,which is a branch of algebra that associates to any ring with unit R a sequence of abelian groups called n-th K-groups of R, denoted by Kn(R). The mid-1950s, Alexander Grothendieck gave a definition of the K0(R) of any ring R. In1962, Hyman Bass and Stephen Schanuel gave the first adequate definition of K1 of any ring R. In 1970, Daniel Quillen gave a general definition of K-groups of any ring R using the +- construction of the classifying space BGL(R). Our interest is the study of the K-groups on the ring of integers OF over a number field F. Using some results of homology of linear groups, this work will give the definition of Borel's regulator map.
 
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Publishing Date
2019-03-22
 
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