AbstractA smooth, projective, absolutely irreducible curve of genus 19 over F2 admitting an infinite S-class field tower is presented. Here S is a set of four F2-rational points on the curve. This is shown to imply that A(2) = limsup # X(F2)/g(X) ≥ 4/(19 − 1) ≈ 0.222. Here the limit is taken over curves X over F2 of genus g(X) → ∞
AbstractWe show that for any finite field Fq, any N⩾0 and all sufficiently large integers g there ex...
In this article we prove lower and upper bounds for class numbers of algebraic curves defined over f...
We study a natural question in the Iwasawa theory of algebraic curves of genus $>1$. Fix a prime num...
AbstractA smooth, projective, absolutely irreducible curve of genus 19 over F2 admitting an infinite...
AbstractFor an algebraic curve X over the finite field Fq, we denote by N(X) and g(X) the number of ...
In this paper we prove that for any prime p and for any p-power q there is a constant C_p > 0 such t...
Minor revisionsFor a given genus $g \geq 1$, we give lower bounds for the maximal number of rational...
AbstractWe discuss the asymptotic behaviour of the genus and the number of rational places in towers...
We discuss the asymptotic behaviour of the genus and the number of rational places in towers of func...
Using Weil descent, we give bounds for the number of rational points on two families of curves over ...
AbstractWe obtain lower bounds for the asymptotic number of rational points of smooth algebraic curv...
We resolve a 1983 question of Serre by constructing curves with many points of every genus over ever...
AbstractIn 1995, Garcia and Stichtenoth explicitly constructed a tower of projective curves over a f...
AbstractWe exhibit a genus-2 curve C defined over Q(T) which admits two independent morphisms to a r...
We push further the classical proof of Weil upper bound for the number of rational points of an abso...
AbstractWe show that for any finite field Fq, any N⩾0 and all sufficiently large integers g there ex...
In this article we prove lower and upper bounds for class numbers of algebraic curves defined over f...
We study a natural question in the Iwasawa theory of algebraic curves of genus $>1$. Fix a prime num...
AbstractA smooth, projective, absolutely irreducible curve of genus 19 over F2 admitting an infinite...
AbstractFor an algebraic curve X over the finite field Fq, we denote by N(X) and g(X) the number of ...
In this paper we prove that for any prime p and for any p-power q there is a constant C_p > 0 such t...
Minor revisionsFor a given genus $g \geq 1$, we give lower bounds for the maximal number of rational...
AbstractWe discuss the asymptotic behaviour of the genus and the number of rational places in towers...
We discuss the asymptotic behaviour of the genus and the number of rational places in towers of func...
Using Weil descent, we give bounds for the number of rational points on two families of curves over ...
AbstractWe obtain lower bounds for the asymptotic number of rational points of smooth algebraic curv...
We resolve a 1983 question of Serre by constructing curves with many points of every genus over ever...
AbstractIn 1995, Garcia and Stichtenoth explicitly constructed a tower of projective curves over a f...
AbstractWe exhibit a genus-2 curve C defined over Q(T) which admits two independent morphisms to a r...
We push further the classical proof of Weil upper bound for the number of rational points of an abso...
AbstractWe show that for any finite field Fq, any N⩾0 and all sufficiently large integers g there ex...
In this article we prove lower and upper bounds for class numbers of algebraic curves defined over f...
We study a natural question in the Iwasawa theory of algebraic curves of genus $>1$. Fix a prime num...
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