Rational points and automorphisms on algebraic curves over finite fields

• Grant number: 16/24713-4
• 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: Nazar Arakelian
• Grantee: Nazar Arakelian
• Host Institution: Centro de Matemática, Computação e Cognição (CMCC). Universidade Federal do ABC (UFABC). Santo André , SP, Brazil
• City of the host institution: Santo André

Abstract

The main objects that will be investigated in this project are the projective algebraic curves defined over finite fields. Here, we investigate the problem of counting rational points on algebraic curves, which includes the construction of maximal curves as well as the study of the Frobenius classicality of plane curves with respect to the linear systems of curves of a given degree. Moreover, the structure of the automorphism group of curves will be investigated. (AU)