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88
Equirépartition des petits points
, 1997
"... Soit E une courbe elliptique sur le corps C des nombres complexes. On note E[n] (resp E[n]) le sous–groupe des points de n–torsion (resp l’ensemble des points d’ordre exactement n). Une simple inspection permet de voir que les points de torsion sont denses dans E pour la topologie de C. Ils sont mêm ..."
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Cited by 42 (4 self)
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Soit E une courbe elliptique sur le corps C des nombres complexes. On note E[n] (resp E[n]) le sous–groupe des points de n–torsion (resp l’ensemble des points d’ordre exactement n). Une simple inspection permet de voir que les points de torsion sont denses dans E pour la topologie de C. Ils sont même équidistribués
Arithmetic height functions over finitely generated fields
 Inventiones Mathematicae 140
, 2000
"... ABSTRACT. In this paper, we propose a new height function for a variety defined over a finitely generated field over Q. For this height function, we will prove Northcott’s theorem and Bogomolov’s conjecture, so that we can recover the original Raynaud’s theorem (ManinMumford’s conjecture). CONTENTS ..."
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Cited by 37 (10 self)
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ABSTRACT. In this paper, we propose a new height function for a variety defined over a finitely generated field over Q. For this height function, we will prove Northcott’s theorem and Bogomolov’s conjecture, so that we can recover the original Raynaud’s theorem (ManinMumford’s conjecture). CONTENTS
Special cycles and derivatives of Eisenstein series, to appear
 in MSRI Proceedings on Rankin Lvalues, arXiv.org/math.NT/0308295. 198 , Derivatives of Eisenstein
, 2002
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Green current for holomorphic automorphisms of compact Kähler manifolds
 J. Amer. Math. Soc
"... Let f be a holomorphic automorphism of a compact Kähler manifold (X, ω) of dimension k ≥ 2. We study the convex cones of positive closed (p, p)currents Tp, which satisfy a functional relation f ∗ Tp = λTp, λ> 1 and some regularity condition (PLB). Under appropriate assumptions on dynamical degre ..."
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Cited by 29 (7 self)
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Let f be a holomorphic automorphism of a compact Kähler manifold (X, ω) of dimension k ≥ 2. We study the convex cones of positive closed (p, p)currents Tp, which satisfy a functional relation f ∗ Tp = λTp, λ> 1 and some regularity condition (PLB). Under appropriate assumptions on dynamical degrees we introduce closed finite dimensional cones, not reduced to zero, of such currents. In particular, when the topological entropy h(f) of f is positive, then for some m ≥ 1, there is a positive closed (m, m)current Tm which satisfies the relation f ∗ Tm = exp(h(f))Tm. Moreover, every quasip.s.h. function is integrable with respect to the trace measure of Tm. When the dynamical degrees of f are all distinct, we construct an invariant measure µ as an intersection of closed currents. We show that this measure is mixing and gives no mass to pluripolar sets and to sets of small Hausdorff dimension. The construction of Tm can be extended to open holomorphic map or regular holomorphic correspondences. We also study the connection between the Julia set of f and the support of invariant (1, 1)currents. For that purpose, we introduce the controlspace of a closed current. 1
A fixed point formula of Lefschetz type in Arakelov geometry II: a residue . . .
, 2008
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Integrals of Borcherds forms
, 2001
"... Let V be a nondegenerate inner product space over Q of signature (n, 2), and let D be the space of oriented negative 2planes in V (R). In [2], Borcherds constructed certain meromorphic modular forms Ψ(F) on D with respect to arithmetic subgroups ΓM of G = O(V) by regularizing ..."
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Cited by 23 (1 self)
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Let V be a nondegenerate inner product space over Q of signature (n, 2), and let D be the space of oriented negative 2planes in V (R). In [2], Borcherds constructed certain meromorphic modular forms Ψ(F) on D with respect to arithmetic subgroups ΓM of G = O(V) by regularizing
Superpotentials of positive closed currents, intersection theory and dynamics
, 2007
"... We introduce a notion of superpotential for positive closed currents of bidegree (p,p) on projective spaces. This permits to obtain a calculus on positive closed currents of arbitrary bidegree. We define in particular the intersection of currents of arbitrary bidegree and the pullback operator by ..."
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Cited by 19 (4 self)
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We introduce a notion of superpotential for positive closed currents of bidegree (p,p) on projective spaces. This permits to obtain a calculus on positive closed currents of arbitrary bidegree. We define in particular the intersection of currents of arbitrary bidegree and the pullback operator by meromorphic maps. One of the main tools is the introduction of structural discs in the space of positive closed currents which gives a “geometry ” on that space. We apply the theory of superpotentials to construct Green currents for rational maps and to study equidistribution problems for holomorphic endomorphisms and for polynomial automorphisms. AMS classification: 37F, 32H50, 32U40. Keywords: superpotential, structural disc of currents, intersection theory, pullback operator, complex dynamics, regular polynomial automorphism, algebraically pstable maps.