Algebraic curves over finite fields

• Grant number: 17/04681-3
• Support Opportunities: Regular Research Grants
• Start date: June 01, 2017
• End date: May 31, 2019
• 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

Abstract

This proposal establishes my research plans for the next two years or so. The core of the investigation are aspects the theory of curves over FiniteFields that are directly related to the number and nature of rational pointson such curves. (AU)

Scientific publications

(8)

(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)

ABDON, MIRIAM; BORGES, HERIVELTO; QUOOS, LUCIANE. Weierstrass points on Kummer extensions. ADVANCES IN GEOMETRY, v. 19, n. 3, p. 323-333, JUL 2019. (17/04681-3)

BORGES, HERIVELTO; COOK, GARY; COUTINHO, MARIANA. Plane sections of Fermat surfaces over finite fields. FINITE FIELDS AND THEIR APPLICATIONS, v. 52, p. 156-173, JUL 2018. (17/04681-3)

BORGES, HERIVELTO; COUTINHO, MARIANA. On some generalized Fermat curves and chords of an affinely regular polygon inscribed in a hyperbola. Journal of Pure and Applied Algebra, v. 224, n. 1, p. 239-249, JAN 2020. (17/04681-3)

BORGES, HERIVELTO; CONCEICAO, RICARDO. A new family of Castle and Frobenius nonclassical curves. Journal of Pure and Applied Algebra, v. 222, n. 4, p. 994-1002, APR 2018. (17/04681-3)

BORGES FILHO, HERIVELTO MARTINS; CASTELLANOS, ALONSO SEPULVEDA; TIZZIOTTI, GUILHERME CHAUD. Subcovers and Codes on a Class of Trace-Defining Curves. IEEE TRANSACTIONS ON INFORMATION THEORY, v. 65, n. 4, p. 2101-2106, APR 2019. (17/04681-3)

BORGES, HERIVELTO; FUKASAWA, SATORU. Galois points for double-Frobenius nonclassical curves. FINITE FIELDS AND THEIR APPLICATIONS, v. 61, JAN 2020. (17/04681-3)

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)

BARTOLI, DANIELE; BORGES, HERIVELTO; QUOOS, LUCIANE. Rational functions with small value set. Journal of Algebra, v. 565, p. 16-pg., 2021-01-01. (17/04681-3)