Let X be a smooth projective connected algebraic curve of genus g defined over an algebraically closed field k of characteristic p > 0. In this paper we study necessary and sufficient conditions for… (More)

Let C be a smooth projective curve defined over a number field k, A/k(C) an abelian variety and (τ, B) the k(C)/k-trace of A. We estimate how the rank of A(k(C))/τB(k) varies when we take a finite… (More)

Let C be a smooth projective irreducible curve of genus g defined over a finite field Fq. Let ∞ be a fixed place of the function field Fq(C) of C. We prove analogues of Lehmer’s conjecture for a… (More)

Let C be a smooth irreducible projective curve defined over a finite field Fq of q elements of characteristic p > 3 andK = Fq(C) its function field and φE : E → C the minimal regular model of E/K.… (More)

Let k be a field of characteristic q, C a smooth connected curve defined over k with function field K := k(C). Let A/K be a non constant abelian variety defined over K of dimension d. We assume that… (More)

Let C be a smooth projective curve defined over a number field k, X/k(C) a smooth projective curve of positive genus, JX the Jacobian variety of X and (τ, B) the k(C)/k-trace of JX . We estimate how… (More)

Let X be a smooth projective connected curve of genus g ≥ 2 defined over an algebraically closed field k of characteristic p > 0. Let G be a finite group, P a Sylow p-subgroup of G and NG(P ) its… (More)

Let C be a smooth projective irreducible curve defined over a finite field Fq of q elements and characteristic p > 3 with function field K = Fq(C). Let E/K be a non-constant elliptic curve and φ : E… (More)