Twists and generalized Zolotarev polynomials

Abstract

A generalization of the so-called Zolotarev polynomial is investigated though the theory of twists and that of generalized Jacobian varieties. As an application, extremal properties, rationality, and a relation with multigrades are revealed.

Relative Manin–Mumford for Semi-Abelian Surfaces

“…Then, p is the projection to E of the section s of G ρ defined (via strict equivalence) above, and one checks that p is not a torsion section. By [20], [31] (see also [15], Prop. 3.1), the Pell equation for Q λ (x) has a non trivial solution if and only if p(λ) is a torsion point on E λ , i.e.…”

“…Then, p is the projection to E of the section s of G ρ defined (via strict equivalence) above, and one checks that p is not a torsion section. By [20], [31] (see also [15] λ (ρ(λ)) ofC. Now, in the first case ρ(λ) = 0, q is a non torsion section, i.e.…”

Generalized jacobians and Pellian polynomials

“…[18], 3.2.3, [4], 3.1) : all the sparse sets we will meet in the present paper have bounded height. See [19] for a general survey on these problems, and [10], [8], for connections with the arithmetic case and with Zolotarev polynomials. Now, what happens if the curve under study has a singularity?…”