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Master's Dissertation
DOI
https://doi.org/10.11606/D.45.2019.tde-15082019-075031
Document
Author
Full name
Fernando Garcia Yamauti
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2019
Supervisor
Committee
Chestakov, Ivan (President)
Arndt, Peter
Logachev, Dmitry
Title in Portuguese
The form of (co)homology
Keywords in Portuguese
Cohomologia
Geometria algébrica
Homologia
Motivos
Teoria de homotopia
Teoria de homotopia motívica
Abstract in Portuguese
Este trabalho é um panorama sobre algumas das principais idéias presentes na teoria dos motivos. Abordando via ponto de vista histórico, o autor convida o leitor a uma dialética em direção à Idéia que pervade as teorias da cohomologia presentes na geometria algébrica: o motivo. Percorrendo desde o sonho sobre cohomologias provindo das Conjecturas de Weil seguida pela imediata frustração das Conjecturas Standard ao jubilo de suprassumir até a teoria de A¹-homotopia de Voevodsky, o autor infunde misticismo na epifania de Grothendieck sobre uma estrutura eterna e imanente engendrando todo o mundo (co)homológico.
Title in English
The form of (co)Homology
Keywords in English
Algebraic geometry
Cohomology
Homology
Homotopy Theory
Motives
Motivic homotopy theory
Abstract in English
This work is a survey in some of the main ideas in the theory of motives. Approaching from an historical point of view, the author invites the reader into a dialectics towards the Idea that pervades cohomology theories in algebraic geometry: the motive. From the dream of those cohomologies arising from Weil's Conjectures and forthwith frustration by the Standard Conjectures to the elation of sublating to Voevodsky's A¹-homotopy theory, the author infuses mysticism in Grothendieck's epiphany of an eternal immanent structure engendering all the (co)homological world.
 
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Publishing Date
2023-01-04
 
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