Algebraic curves over finite fields

• Grant number: 11/19446-3
• Support Opportunities: Regular Research Grants
• Start date: January 01, 2012
• End date: March 31, 2014
• 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
• City of the host institution: São Carlos

Abstract

This project aims to obtain and characterizenew algebraic curves over finite fields and with many rational points. It also includes the study of a very special class of polynomials that, despite of being interesting on its own,turned out to be the key ingredient in the study of Frobenius non-classical curves. The arc property of curves attaining the Hasse-Weil boundis also considered in our study. Application in Coding Theory is one of the motivations of this work. (AU)

Scientific publications

(4)

(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; CONCEICAO, RICARDO. On the characterization of minimal value set polynomials. JOURNAL OF NUMBER THEORY, v. 133, n. 6, p. 2021-2035, JUN 2013. (11/19446-3)

ARAKELIAN, NAZAR; BORGES, HERIVELTO. Frobenius nonclassicality with respect to linear systems of curves of arbitrary degree. ACTA ARITHMETICA, v. 167, n. 1, p. 43-66, 2015. (11/19446-3, 13/00564-1)

BORGES, HERIVELTO; MOTTA, BEATRIZ; TORRES, FERNANDO. Complete arcs arising from a generalization of the Hermitian curve. ACTA ARITHMETICA, v. 164, n. 2, p. 101-118, 2014. (11/19446-3)

BORGES, HERIVELTO. Frobenius nonclassical components of curves with separated variables. JOURNAL OF NUMBER THEORY, v. 159, p. 402-425, FEB 2016. (11/19446-3)