Rational points on algebraic curves over finite fields

• Grant number: 14/03497-6
• Support Opportunities: Scholarships abroad - Research Internship - Post-doctor
• Start date: August 10, 2014
• End date: February 09, 2015
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Fernando Eduardo Torres Orihuela
• Grantee: Nazar Arakelian
• Supervisor: Gábor Korchmáros
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Institution abroad: Università degli Studi della Basilicata, Italy
• Associated to the scholarship: 13/00564-1 - Rational points on algebraic curves over finite fields., BP.PD

Abstract

The purpose of this project is to study the problem of estimating the number of rational points on algebraic curves defined over finite fields. Consider a projective, irreducible, non-singular, algebraic curve defined over a finite field Fq. Upper bounds for the number of Fq-rational points of the curve are obtained via the Stohr-Voloch theory applied to some non-complete linear series. For a plane curve with a peculiar property, the bounds obtained in such way improve some other known bounds of literature.The main goals here are the following:-Characterize the equation of the plane curves having such aforementioned property.-Develop methods to obtain a plane model with such property from a given curve.- Present examples and applications. (AU)

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)

ARAKELIAN, NAZAR; KORCHMAROS, GABOR. A characterization of the Artin-Mumford curve. JOURNAL OF NUMBER THEORY, v. 154, p. 278-291, SEP 2015. (14/03497-6)