Elliptic curves: arithmetic and computation
- Start Date
- 2019-02-11
- End Date
- 2019-02-22
- Institution
- Universidad de la República
- City
- Montevideo
- Country
- Uruguay
- Meeting Type
- CIMPA school
- Homepage
- http://www.rnta.eu/Montevideo2019/
- Contact Name
- Valerio Talamanca
- Created
- Modified
Description
The aim of this is school to introduce the participants to the arithmetic and computational aspects of the theory of elliptic curves. Elliptic curves lie at the crossroads of algebra, analysis, geometry and arithmetic. We will develop the theory of elliptic curves from its very beginning also providing an introductory course on algebraic curves and the Riemann Roch theorem. Topics that will be covered include: basic geometric and arithmetic results for elliptic curves over number fields and over finite fields, the Mordell-Weil theorem for elliptic curves, Galois representations attached to elliptic curves,. and the Birch and Swinnerton Dyer Conjecture. On the computational side we will run six hours of training sessions on PARI/GP and SAGE.
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