Advanced search
Start date
Betweenand
Related content

Rational points on algebraic curves over finite fields.

Grant number: 13/00564-1
Support Opportunities:Scholarships in Brazil - Post-Doctoral
Effective date (Start): July 01, 2013
Effective date (End): February 11, 2016
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Algebra
Principal Investigator:Fernando Eduardo Torres Orihuela
Grantee:Nazar Arakelian
Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
Associated scholarship(s):14/03497-6 - Rational points on algebraic curves over finite fields, BE.EP.PD

Abstract

The purpose of this project is to study the problem of counting rational points on algebraiccurves dened over finite fields. Related to this problem, we will study the Frobeniusclassicality of plane algebraic curves over finite fields with respect to linear systems ofcurves of a certain degree. More specically, we will investigate the following topics: -Bounds to rational points on algebraic curves over finite fields; -Frobenius classicality of algebraic curves over finite fields, with emphasis on Fermatcurves and on the curves presented in the PhD thesis of the candidate.A great part of this project is a natural continuation of the research line developed bythe candidate during his PhD.

News published in Agência FAPESP Newsletter about the scholarship:
More itemsLess items
Articles published in other media outlets ( ):
More itemsLess items
VEICULO: TITULO (DATA)
VEICULO: TITULO (DATA)

Scientific publications (6)
(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; BORGES, HERIVELTO. Frobenius nonclassicality with respect to linear systems of curves of arbitrary degree. ACTA ARITHMETICA, v. 167, n. 1, p. 43-66, . (11/19446-3, 13/00564-1)
ARAKELIAN, NAZAR; BORGES, HERIVELTO. Bounds for the number of points on curves over finite fields. Israel Journal of Mathematics, v. 228, n. 1, p. 177-199, . (15/03984-7, 13/00564-1)
ARAKELIAN, NAZAR; SPEZIALI, PIETRO. On generalizations of Fermat curves over finite fields and their automorphisms. COMMUNICATIONS IN ALGEBRA, v. 45, n. 11, p. 4926-4938, . (13/00564-1)
ARAKELIAN, NAZAR; TAFAZOLIAN, SAEED; TORRES, FERNANDO. ON THE SPECTRUM FOR THE GENERA OF MAXIMAL CURVES OVER SMALL FIELDS. Advances in Mathematics of Communications, v. 12, n. 1, p. 143-149, . (13/00564-1)
ARAKELIAN, NAZAR. Number of rational branches of a singular plane curve over a finite field. FINITE FIELDS AND THEIR APPLICATIONS, v. 48, p. 87-102, . (13/00564-1)
ARAKELIAN, NAZAR; BORGES, HERIVELTO. FROBENIUS NONCLASSICALITY OF FERMAT CURVES WITH RESPECT TO CUBICS. Israel Journal of Mathematics, v. 218, n. 1, p. 273-297, . (13/00564-1)

Please report errors in scientific publications list using this form.