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Audiovisual Mathematics Library

Audiovisual Mathematics Library

Documents Voloch, José Felipe 4 results

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Generators of elliptic curves over finite fields - Voloch, José Felipe (Author of the conference) | CIRM H

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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.

11G20 ; 14H52 ; 11Y16 ; 11T23

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Differential descent obstructions - Voloch, José Felipe (Author of the conference) | CIRM H

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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.

11G35 ; 14G17

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Maps between curves and diophantine obstructions - Voloch, José Felipe (Author of the conference) | CIRM H

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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 ...[+]

11G20 ; 11G35 ; 14G05

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Factoring polynomials over function fields - Voloch, José Felipe (Author of the conference) | CIRM H

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If $K$/$k$ is a function field in one variable of positive characteristic, we describe a general algorithm to factor one-variable polynomials with coefficients in $K$. The algorithm is flexible enough to find factors subject to additional restrictions, e.g., to find all roots that belong to a given finite dimensional $k$-subspace of $K$ more efficiently. This has an application to list decoding of AG codes that we also describe.

12Y05 ; 11R09 ; 11T71

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