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Journals and Conferences
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 a finite group G to be a quotient of the algebraic fundamental group π1(X) of X. We denote by πA(X) the set of isomorphism classes of finite groups which are… (More)
Using 22 pb 1 of data collected at LEP in 1992 on the peak of the Z resonance, the ALEPH collaboration has measured the polarisation of the tau leptons decaying into e , , , and a1 from their individual decay product distributions. The measurement of the tau polarisation as a function of the production polar angle yields the two parameters A and Ae, where,… (More)
Let π1(C) be the algebraic fundamental group of a smooth connected affine curve, defined over an algebraically closed field of characteristic p > 0 of countable cardinality. Let N be a normal (resp. characteristic) subgroup of π1(C). Under the hypothesis that the quotient π1(C)/N admits an infinitely generated Sylow p-subgroup, we prove that N is indeed… (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 Galois k-cover π : C → C defined over k.
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 Drinfeld module φ defined over a finite extension of Fq(C) with integral coefficients. More precisely, if ĥφ is the canonical height of φ and α is a non-torsion… (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. For each P ∈ C denote EP = φ −1 E (P ). The elliptic curve E/K has good reduction at P ∈ C if and only if EP is an elliptic curve defined over the residue field… (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 q = 0 or > 2d + 1. Let p 6= q be a prime number and C → C a finite geometrically Galois and étale cover defined over k with function field K ′ := k(C). Let (τ ,… (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 the rank of JX(k(C))/τB(k) varies when we take an unramified abelian cover π : C ′ → C defined over k.
Baryon Acoustic Oscillations (BAO) provide a standard ruler of known physical length, making it one of the most promising probes of the nature of dark energy. The detection of BAO as an excess of power in the galaxy distribution at a certain scale requires measuring galaxy positions and redshifts. Transversal (or angular ) BAO measure the angular size of… (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 normalizer in G. We show that if there exists an étale Galois cover Y → X with group NG(P ), then G is the Galois group wan étale Galois cover Y → X , where the… (More)