Algebraic Curves over Finite Fields

• Grant number: 18/23839-0
• Support Opportunities: 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 Investigator: Herivelto Martins Borges Filho
• Grantee: Mariana de Almeida Nery Coutinho
• Host 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.

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. (18/23839-0, 17/04681-3)