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Master's Dissertation
DOI
10.11606/D.55.2018.tde-23072018-145841
Document
Author
Full name
Alex Freitas de Campos
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2017
Supervisor
Committee
Borges Filho, Herivelto Martins (President)
Arakelian, Nazar
Conte, Luciane Quoos
Levcovitz, Daniel
Title in Portuguese
Corpos de funções algébricas sobre corpos finitos
Keywords in Portuguese
Corpos finitos
Extensões de Artin-Schreier
Pontos racionais
Abstract in Portuguese
Este trabalho é essencialmente sobre pontos racionais em curvas algébricas sobre corpos finitos ou, equivalentemente, lugares racionais em corpos de funções algébricas em uma variável sobre corpos finitos. O objetivo é a demonstração da existência de constantes aq e bq ∈ R> 0 tais que se g ≥ aq. N + bq, então existe uma curva sobre Fq de gênero g com N pontos racionais.
Title in English
Algebraic Function Fields over finite fields
Keywords in English
Artin-Schreier extensions
Finite fields
rational points
Abstract in English
This work is essentially about rational points on algebraic curves over finite fields or, equivalently, rational places on algebraic function fields of one variable over finite fields. The aim is the proof of the existence of constants aq and bq ∈ R> 0 such that if g ≥ aq ∈ aq . N+bq then there exists a curve over Fq of genus g with N rational points.
 
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Publishing Date
2018-07-23
 
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