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# Résultats de recherche

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## E. Peyre - Slopes and distribution of points (part2)

The distribution of rational points of bounded height on algebraic varieties is far from uniform. Indeed the points tend to accumulate on thin subsets which are images of non-trivial finite morphisms. The problem is to find a way to characterise these thin subsets. The slopes introduced by Jean-Benoît Bost are a useful tool for this problem. These lectures will present several cases in which this approach is fruitful. We shall also describe the notion of locally accumulating subvarieties which arise when one considers rational points of ... Voir la vidéole (1h10s)

## D. Loughran - Sieving rational points on algebraic varieties

Sieves are an important tool in analytic number theory. In a typical sieve problem, one is given a list of p-adic conditions for all primes p, and the challenge is to count the number of integers which satisfy all these p-adic conditions. In this talk we present some versions of sieves for varieties whose rational points are equidistributed, and give applications to counting rational points in thin sets. This is joint work with Tim Browning. Voir la vidéole (1h31m53s)

## A. Chambert-Loir - Equidistribution theorems in Arakelov geometry and Bogomolov conjecture (part3)

Let X be an algebraic curve of genus g⩾2 embedded in its Jacobian variety J. The Manin-Mumford conjecture (proved by Raynaud) asserts that X contains only finitely many points of finite order. When X is defined over a number field, Bogomolov conjectured a refinement of this statement, namely that except for those finitely many points of finite order, the Néron-Tate heights of the algebraic points of X admit a strictly positive lower bound. This conjecture has been proved by Ullmo, and an extension to all subvarieties ... Voir la vidéole (1h32m37s)

## R. Dujardin - Some problems of arithmetic origin in complex dynamics and geometry (part3)

Some themes inspired from number theory have been playing an important role in holomorphic and algebraic dynamics (iteration of rational mappings) in the past ten years. In these lectures I would like to present a few recent results in this direction. This should include: the dynamical Manin-Mumford problem, in particular in the case of product rational maps (P(x),Q(y)) (after Ghioca, Nguyen, and Ye) the “unlikely intersection” problem (after Baker and DeMarco, and also Favre and ... Voir la vidéole (55m57s)

## E. Peyre - Slopes and distribution of points (part3)

The distribution of rational points of bounded height on algebraic varieties is far from uniform. Indeed the points tend to accumulate on thin subsets which are images of non-trivial finite morphisms. The problem is to find a way to characterise these thin subsets. The slopes introduced by Jean-Benoît Bost are a useful tool for this problem. These lectures will present several cases in which this approach is fruitful. We shall also describe the notion of locally accumulating subvarieties which arise when one considers rational points of ... Voir la vidéole (1h2m27s)

## Z. Huang - Diophantine approximation and local distribution of rational points

We show how to use the recent work of D. McKinnon and M. Roth on generalizations of Diophantine approximation to algebraic varieties to formulate a local version of the Batyrev-Manin principle on the distribution of rational points. We present several toric varieties for which the result is known. Voir la vidéole (59m43s)

## A. Chambert-Loir - Equidistribution theorems in Arakelov geometry and Bogomolov conjecture (part4)

Let X be an algebraic curve of genus g⩾2 embedded in its Jacobian variety J. The Manin-Mumford conjecture (proved by Raynaud) asserts that X contains only finitely many points of finite order. When X is defined over a number field, Bogomolov conjectured a refinement of this statement, namely that except for those finitely many points of finite order, the Néron-Tate heights of the algebraic points of X admit a strictly positive lower bound. This conjecture has been proved by Ullmo, and an extension to all subvarieties ... Voir la vidéole (1h28m48s)

## E. Peyre - Slopes and distribution of points (part4)

The distribution of rational points of bounded height on algebraic varieties is far from uniform. Indeed the points tend to accumulate on thin subsets which are images of non-trivial finite morphisms. The problem is to find a way to characterise these thin subsets. The slopes introduced by Jean-Benoît Bost are a useful tool for this problem. These lectures will present several cases in which this approach is fruitful. We shall also describe the notion of locally accumulating subvarieties which arise when one considers rational points of ... Voir la vidéole (1h2m21s)