2017

The goal of this talk is to introduce a Gross--Zagier type formula, which relates the arithmetic self-intersection number of the Hodge bundle of a quaternionic Shimura curve over a totally real

Chavdarov and Zywina showed that after passing to a suitable field extension, every abelian surface A with real multiplication over some number field has geometrically simple reduction modulo p

For any Fuchsian subgroup Γ⊂PSL2(R) of the first kind, Selberg introduced the Selberg zeta function in analogy to the Riemann zeta function using the lengths of simple closed geodesics on Γ∖H

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

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

Let X be a 2-dimensional, normal, flat, proper scheme over the integers. Assume ¯L and ¯M are two hermitian line bundles over X. Arakelov (and Deligne) defined a real number ¯L.¯M, the arithmetic

Let X be a 2-dimensional, normal, flat, proper scheme over the integers. Assume ¯L and ¯M are two hermitian line bundles over X. Arakelov (and Deligne) defined a real number ¯L.¯M, the arithmetic

Let X be a 2-dimensional, normal, flat, proper scheme over the integers. Assume ¯L and ¯M are two hermitian line bundles over X. Arakelov (and Deligne) defined a real number ¯L.¯M, the arithmetic

Let X be a 2-dimensional, normal, flat, proper scheme over the integers. Assume ¯L and ¯M are two hermitian line bundles over X. Arakelov (and Deligne) defined a real number ¯L.¯M, the arithmetic

Let X be a subvariety of Pn defined over a number field and N(B) be the number of rational points of height at most B on X. There are then general conjectures of Manin on the asymptotic behaviour

Let X be a subvariety of Pn defined over a number field and N(B) be the number of rational points of height at most B on X. There are then general conjectures of Manin on the asymptotic behaviour

Let X be a subvariety of Pn defined over a number field and N(B) be the number of rational points of height at most B on X. There are then general conjectures of Manin on the asymptotic behaviour

Let X be a subvariety of Pn defined over a number field and N(B) be the number of rational points of height at most B on X. There are then general conjectures of Manin on the asymptotic behaviour

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

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

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

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

Ce cours présente un abrégé de la théorie des minima et pentes successives des espaces adéliques rigides sur une extension algébrique du corps des nombres rationnels. Seront réunis dans un même

Ce cours présente un abrégé de la théorie des minima et pentes successives des espaces adéliques rigides sur une extension algébrique du corps des nombres rationnels. Seront réunis dans un même

Ce cours présente un abrégé de la théorie des minima et pentes successives des espaces adéliques rigides sur une extension algébrique du corps des nombres rationnels. Seront réunis dans un même

In these lectures I will focus on the Riemann-Roch theorem in Arakelov geometry, in the specific context of some simple Shimura varieties. For suitable data, the cohomological part of the theorem

In these lectures I will focus on the Riemann-Roch theorem in Arakelov geometry, in the specific context of some simple Shimura varieties. For suitable data, the cohomological part of the theorem

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

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

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

Le théorème de Hilbert-Samuel en géométrie algébrique relie le comportement asymptotique du système linéaire gradué d’un faisceau inversible ample au nombre d’intersection. Gillet et Soulé ont

Le théorème de Hilbert-Samuel en géométrie algébrique relie le comportement asymptotique du système linéaire gradué d’un faisceau inversible ample au nombre d’intersection. Gillet et Soulé ont

Le théorème de Hilbert-Samuel en géométrie algébrique relie le comportement asymptotique du système linéaire gradué d’un faisceau inversible ample au nombre d’intersection. Gillet et Soulé ont

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.

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.

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.

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.

A Shimura variety is a higher-dimensional analogue of a modular curve that arises as a quotient of a Hermitian symmetric space by a congruence subgroup of a reductive algebraic group defined over

A Shimura variety is a higher-dimensional analogue of a modular curve that arises as a quotient of a Hermitian symmetric space by a congruence subgroup of a reductive algebraic group defined over

In the classical analogy between number fields and function fields, an Euclidean lattice (E,∥.∥) may be seen as the counterpart of a vector bundle V on a smooth projective curve C over some field

In the classical analogy between number fields and function fields, an Euclidean lattice (E,∥.∥) may be seen as the counterpart of a vector bundle V on a smooth projective curve C over some field

We will first introduce Shimura varieties of orthogonal type, their Heegner divisors and some special points, called CM (Complex Multiplication) points. Secondly we will review conjectures of

We will first introduce Shimura varieties of orthogonal type, their Heegner divisors and some special points, called CM (Complex Multiplication) points. Secondly we will review conjectures of

We will first introduce Shimura varieties of orthogonal type, their Heegner divisors and some special points, called CM (Complex Multiplication) points. Secondly we will review conjectures of

We will first introduce Shimura varieties of orthogonal type, their Heegner divisors and some special points, called CM (Complex Multiplication) points. Secondly we will review conjectures of

We will first introduce Shimura varieties of orthogonal type, their Heegner divisors and some special points, called CM (Complex Multiplication) points. Secondly we will review conjectures of