Finite geometry, Algebraic curves and Applications to Coding Theory
Algebraic curves in positive characteristic and applications
Curves with many rational points over finite fields and their applications in cod...
| 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 |
Abstract
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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