On the quantity of elliptic curves satisfying the Birch and Swinnerton-Dyer conjecture

• Grant number: 19/07386-8
• Support Opportunities: Scholarships in Brazil - Master
• Start date: August 01, 2019
• End date: May 31, 2020
• 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 will study properties of elliptic curves over Q, their associated Tate-Shafarevich groups and Selmer groups, with an eye towards a result by Bhargava-Skinner-Zhang (2014) which states that the majority (over 66 percent) of such elliptic curves, when ordered by height, satisfies the Birch and Swinnerton-Dyer conjecture, one of the main open problems in modern Number Theory.

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

WALCHEK, Eduardo Rocha. On the quantity of elliptic curves satisfying the Birch and Swinnerton-Dyer conjecture. 2020. Master's Dissertation - Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) São Carlos.