Hecke operators, the Eichler-Shimura relation and an introduction to modularity

• Grant number: 18/08474-5
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: June 01, 2018
• End date: November 30, 2018
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Algebra
• Principal Investigator: Herivelto Martins Borges Filho
• Grantee: Eduardo Rocha Walchek
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

In this project, we propose to study topics of the theory of modular forms and Hecke operators, such that Hecke eigenforms, Moduli spaces of elliptic curves over Q, reduction of algebraic curves (elliptic curves, in particular) mod prime, Jacobian and Picard group of modular curves and the connection between this topics with a view to a proof of the Eichler-Shimura relation, as well as its connection with the Modularity Theorem.