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Algebraic curves over finite fields and applications

Grant number: 22/15301-5
Support Opportunities:Regular Research Grants
Duration: April 01, 2023 - March 31, 2025
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Algebra
Principal Investigator:Herivelto Martins Borges Filho
Grantee:Herivelto Martins Borges Filho
Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
Associated researchers: Daniele Bartoli ; Giovanni Zini ; Jose Felipe Voloch ; Ricardo Alberto Podesta ; Yves Aubry


This project deals with algebraic curves over finite fields and their applications.The central theme underlying its development is the study of rational points in algebraic curves over finite fields. This includes obtaining new bounds for the number of rational points as well as characterizing curves reaching such bounds. This theme is transversal to several other relevant themes in the area, each one with its own universe of fundamental questions for the theory. In this way, the project encompasses and is subdivided into several questions that involve arithmetic and geometric aspects of algebraic curves over finite fields. (AU)

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