Minicurso: Curves over a finite field – Herivelto Borges (USP) – 26, 28 de fevereiro e 1 de março
Horário: 14h.
Sala: 407 – Bloco H – Gragoatá.
Professor: Herivelto Borges (USP).
Pré-requisitos: noções básicas sobre corpos finitos e curvas algébricas.
Programação:
• Fq rational places, divisors and linear series.
• The Stöhr-Voloch theorem.
• Frobenius classicality with respect to lines.
• Frobenius classicality with respect to conics.
• The dual of a Frobenius non-classical curve.
• Zeta-function and curves with many rational points.
• The Zeta-function of a curve over a finite field.
• The Hasse-Weil theorem.
• Asymptotic bounds.
• Elliptic curves over Fq.
• Background on maximal curves.
• Castelnuovo’s number.
• Plane maximal curves and maximal curves of Hurwitz type.
• Non-isomorphic maximal curves.
Se o tempo permitir, incluiremos resultados mais recentes.
Referências:
[1] Arakelian N., Borges H., Bounds for the number of points on curves over finite fields, Israel Journal of Math. 228, (2018) 177-199.
[2] Hirschfeld, J.W.P., Korchmáros G., Torres F., Algebraic curves over a finite field, Princeton Series in App. Math., 2008.
[3] Stöhr K.O., Voloch J.F., Weierstrass points and curves over finite fields, Proc. London Math. Soc. 52(1986) 1-19.