Elliptic curves: arithmetic and computation

nt.number-theory
Start Date
2019-02-11 
End Date
2019-02-22 
Institution
Universidad de la Rep├║blica 
City
Montevideo 
Country
Uruguay 
Meeting Type
CIMPA school 
Homepage
http://www.rnta.eu/Montevideo2019/ 
Contact Name
Valerio Talamanca 

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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