On the quantity of elliptic curves satisfying the Birch and Swinnerton-Dyer conjec...
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On the quantity of elliptic curves satisfying the Birch and Swinnerton-Dyer conjecture
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| Author(s): |
Eduardo Rocha Walchek
Total Authors: 1
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| Document type: | Master's Dissertation |
| Press: | São Carlos. |
| Institution: | Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) |
| Defense date: | 2020-05-18 |
| Examining board members: |
Herivelto Martins Borges Filho;
Daniel Levcovitz;
Victor Gonzalo Lopez Neumann;
Eduardo Tengan
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| Advisor: | Herivelto Martins Borges Filho |
| Abstract | |
In this work, we studied properties of elliptic curves over Q, their associated TateShafarevich groups and Selmer groups, with an eye towards a result by Bhargava, Skinner e Zhang (2014, p. 1, Theorem 1) 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. (AU) | |
| FAPESP's process: | 19/07386-8 - On the quantity of elliptic curves satisfying the Birch and Swinnerton-Dyer conjecture |
| Grantee: | Eduardo Rocha Walchek |
| Support Opportunities: | Scholarships in Brazil - Master |