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Algebraic Curves over Finite Fields

Grant number: 18/23839-0
Support type:Scholarships in Brazil - Post-Doctorate
Effective date (Start): April 01, 2019
Effective date (End): March 31, 2022
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Algebra
Principal researcher:Herivelto Martins Borges Filho
Grantee:Mariana de Almeida Nery Coutinho
Home Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

Inserted in the context of algebraic curves defined over finite fields, which constitutes nowadays a broad area of study and research, especially because of its applications on coding theory and cryptography, the present project aims to investigate some aspects related to these mathematical objects. More precisely, continuing the studies carried out during the candidate's doctorate, here we propose to develop the research comprising the following main topics: 1. Plane sections of Fermat surfaces over finite fields.2. Bounds for the number of Fq-rational points on aX^nY^n-X^n-Y^n+b=0 and the Fq-Frobenius classicality of some related linear series.3. Some properties of the generalized Suzuki curve.

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Scientific publications
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
BORGES, HERIVELTO; COUTINHO, MARIANA. ON THE ZETA FUNCTION AND THE AUTOMORPHISM GROUP OF THE GENERALIZED SUZUKI CURVE. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, v. 374, n. 3, p. 1899-1917, MAR 2021. Web of Science Citations: 0.

Please report errors in scientific publications list by writing to: cdi@fapesp.br.