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# Documents  Voloch, José Felipe | enregistrements trouvés : 4

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## Generators of elliptic curves over finite fields Voloch, José Felipe | CIRM H

Multi angle

Research talks;Algebraic and Complex Geometry;Number Theory

We will discuss some problems and results connected with finding generators for the group of rational points of elliptic curves over finite fields and connect this with the analogue for elliptic curves over function fields of Artin’s conjecture for primitive roots.

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## Differential descent obstructions Voloch, José Felipe | CIRM H

Multi angle

Research talks;Algebraic and Complex Geometry;Number Theory

We will discuss a new obstruction to the existence of rational and integral points on algebraic varieties over function fields obtained by considering covers described by differential equations.

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## Maps between curves and diophantine obstructions Voloch, José Felipe | CIRM H

Multi angle

Research talks;Algebraic and Complex Geometry;Number Theory

Given two algebraic curves $X$, $Y$ over a finite field we might want to know if there is a rational map from $Y$ to $X$. This has been looked at from a number of perspectives and we will look at it from the point of view of diophantine geometry by viewing the set of maps as $X(K)$ where $K$ is the function field of $Y$. We will review some of the known obstructions to the existence of rational points on curves over global fields, apply them to this situation and present some results and conjectures that arise. Given two algebraic curves $X$, $Y$ over a finite field we might want to know if there is a rational map from $Y$ to $X$. This has been looked at from a number of perspectives and we will look at it from the point of view of diophantine geometry by viewing the set of maps as $X(K)$ where $K$ is the function field of $Y$. We will review some of the known obstructions to the existence of rational points on curves over global fields, apply them to ...

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## Códigos corretores de erros16e colóquio brasileiro de matemática Voloch, José Felipe | Instituto de Matemática Pura e Aplicada

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code MDS # code correcteur d'erreur # code cyclique # code de Goppa # géométrie finie

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