Abstract. We consider the generation of prime-order elliptic curves (ECs) over a prime field Fp u... more Abstract. We consider the generation of prime-order elliptic curves (ECs) over a prime field Fp using the Complex Multiplication (CM) method. A crucial step of this method is to compute the roots of a special type of class field polynomials with the most commonly used being the Hilbert and Weber ones. These polynomials are uniquely determined by the CM discriminant D. In this paper, we consider a variant of the CM method for constructing elliptic curves (ECs) of prime order using Weber polynomials. In attempting to construct prime-order ECs using Weber polynomials, two difficulties arise (in addition to the necessary transformations of the roots of such polynomials to those of their Hilbert counterparts). The first one is that the requirement of prime order necessitates that D ≡ 3 (mod 8), which gives Weber polynomials with degree ∗ This work was partially supported by the IST Programme of EU under contracts no. IST-2001-33116 (FLAGS), and by the Action IRAKLITOS (Fellowships for Re...
The automorphism group of the generalized Fermat $F_{k,n}$ curves is studied. We use tools from t... more The automorphism group of the generalized Fermat $F_{k,n}$ curves is studied. We use tools from the theory of complete projective intersections in order to prove that every automorphism of the curve can be extended to an automorphism of the ambient projective space. In particular if $k-1$ is not a power of the characteristic, then a conjecture of of Y. Fuertes, G. Gonz\'alez-Diez, R. Hidalgo, M. Leyton is proved.
ABSTRACT We give a criterion, based on the automorphism group, for certain cyclic covers of the p... more ABSTRACT We give a criterion, based on the automorphism group, for certain cyclic covers of the projective line to be defined over their field of moduli. An example of a cyclic cover of the complex projective line with field of moduli ℝ that can not be defined over ℝ is given
ABSTRACT This paper has been withdrawn by the author. The main result is wrong, as M.Matignon and... more ABSTRACT This paper has been withdrawn by the author. The main result is wrong, as M.Matignon and C. Lehr provided a counterexample to it.
We use rigid analytic uniformization by Schottky groups to give a bound for the order of the abel... more We use rigid analytic uniformization by Schottky groups to give a bound for the order of the abelian subgroups of the automorphism group of a Mumford curve in terms of its genus.
Abstract. We consider the generation of prime-order elliptic curves (ECs) over a prime field Fp u... more Abstract. We consider the generation of prime-order elliptic curves (ECs) over a prime field Fp using the Complex Multiplication (CM) method. A crucial step of this method is to compute the roots of a special type of class field polynomials with the most commonly used being the Hilbert and Weber ones. These polynomials are uniquely determined by the CM discriminant D. In this paper, we consider a variant of the CM method for constructing elliptic curves (ECs) of prime order using Weber polynomials. In attempting to construct prime-order ECs using Weber polynomials, two difficulties arise (in addition to the necessary transformations of the roots of such polynomials to those of their Hilbert counterparts). The first one is that the requirement of prime order necessitates that D ≡ 3 (mod 8), which gives Weber polynomials with degree ∗ This work was partially supported by the IST Programme of EU under contracts no. IST-2001-33116 (FLAGS), and by the Action IRAKLITOS (Fellowships for Re...
The automorphism group of the generalized Fermat $F_{k,n}$ curves is studied. We use tools from t... more The automorphism group of the generalized Fermat $F_{k,n}$ curves is studied. We use tools from the theory of complete projective intersections in order to prove that every automorphism of the curve can be extended to an automorphism of the ambient projective space. In particular if $k-1$ is not a power of the characteristic, then a conjecture of of Y. Fuertes, G. Gonz\'alez-Diez, R. Hidalgo, M. Leyton is proved.
ABSTRACT We give a criterion, based on the automorphism group, for certain cyclic covers of the p... more ABSTRACT We give a criterion, based on the automorphism group, for certain cyclic covers of the projective line to be defined over their field of moduli. An example of a cyclic cover of the complex projective line with field of moduli ℝ that can not be defined over ℝ is given
ABSTRACT This paper has been withdrawn by the author. The main result is wrong, as M.Matignon and... more ABSTRACT This paper has been withdrawn by the author. The main result is wrong, as M.Matignon and C. Lehr provided a counterexample to it.
We use rigid analytic uniformization by Schottky groups to give a bound for the order of the abel... more We use rigid analytic uniformization by Schottky groups to give a bound for the order of the abelian subgroups of the automorphism group of a Mumford curve in terms of its genus.
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