2017

Mise en ligne : 30 juin 2017
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X. Yuan - On the arithmetic degree of Shimura curves

Vidéos

X. Yuan - On the arithmetic degree of Shimura curves
Conférence
01:00:14
X. Yuan - On the arithmetic degree of Shimura curves
Yuan
Xinyi

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

Y. Tang - Exceptional splitting of reductions of abelian surfaces with real multiplication
Conférence
01:03:00
Y. Tang - Exceptional splitting of reductions of abelian surfaces with real multiplication

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

A. von Pippich - An analytic class number type formula for PSL2(Z)
Conférence
01:01:13
A. von Pippich - An analytic class number type formula for PSL2(Z)
Pippich
Anna-Maria von

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

D. Loughran - Sieving rational points on algebraic varieties
Cours
01:00:09
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

Z. Huang - Diophantine approximation and local distribution of rational points
Cours
01:02:26
Z. Huang - Diophantine approximation and local distribution of rational points
Huang
Zhizhong

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

C. Soulé - Arithmetic Intersection (Part4)
Cours
01:24:42
C. Soulé - Arithmetic Intersection (Part4)
Soulé
Christophe

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

C. Soulé - Arithmetic Intersection (Part3)
Cours
01:26:12
C. Soulé - Arithmetic Intersection (Part3)
Soulé
Christophe

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

C. Soulé - Arithmetic Intersection (Part2)
Cours
01:10:08
C. Soulé - Arithmetic Intersection (Part2)
Soulé
Christophe

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

C. Soulé - Arithmetic Intersection (Part1)
Cours
01:31:49
C. Soulé - Arithmetic Intersection (Part1)
Soulé
Christophe

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

P. Salberger - Quantitative aspects of rational points on algebraic varieties (part4)
Cours
01:29:58
P. Salberger - Quantitative aspects of rational points on algebraic varieties (part4)
Salberger
Per

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

P. Salberger - Quantitative aspects of rational points on algebraic varieties (part3)
Cours
01:24:43
P. Salberger - Quantitative aspects of rational points on algebraic varieties (part3)
Salberger
Per

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

P. Salberger - Quantitative aspects of rational points on algebraic varieties (part2)
Cours
01:03:57
P. Salberger - Quantitative aspects of rational points on algebraic varieties (part2)
Salberger
Per

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

P. Salberger - Quantitative aspects of rational points on algebraic varieties (part1)
Cours
01:04:37
P. Salberger - Quantitative aspects of rational points on algebraic varieties (part1)
Salberger
Per

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

É. Gaudron - Minima et pentes des espaces adéliques rigides (Part 2)
Cours
01:30:59
É. Gaudron - Minima et pentes des espaces adéliques rigides (Part 2)
Gaudron
Eric

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

G.Freixas i Montplet - Automorphic forms and arithmetic intersections (part 3)
Cours
00:46:13
G.Freixas i Montplet - Automorphic forms and arithmetic intersections (part 3)
Freixas i Montplet
Gérard

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

G. Freixas i Montplet - Automorphic forms and arithmetic intersections (part 2)
Cours
01:31:05
G. Freixas i Montplet - Automorphic forms and arithmetic intersections (part 2)
Freixas i Montplet
Gérard

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

R. Dujardin - Some problems of arithmetic origin in complex dynamics and geometry (part3)
Cours
01:32:36
R. Dujardin - Some problems of arithmetic origin in complex dynamics and geometry (part3)
Dujardin
Romain

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

R. Dujardin - Some problems of arithmetic origin in complex dynamics and geometry (part2)
Cours
01:31:00
R. Dujardin - Some problems of arithmetic origin in complex dynamics and geometry (part2)
Dujardin
Romain

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

R. Dujardin - Some problems of arithmetic origin in complex dynamics and geometry (part1)
Cours
01:33:48
R. Dujardin - Some problems of arithmetic origin in complex dynamics and geometry (part1)
Dujardin
Romain

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

A. Chambert-Loir - Equidistribution theorems in Arakelov geometry and Bogomolov conjecture (part4)
Cours
00:59:42
A. Chambert-Loir - Equidistribution theorems in Arakelov geometry and Bogomolov conjecture (part4)
Chambert-Loir
Antoine

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. Chambert-Loir - Equidistribution theorems in Arakelov geometry and Bogomolov conjecture (part3)
Cours
01:31:52
A. Chambert-Loir - Equidistribution theorems in Arakelov geometry and Bogomolov conjecture (part3)
Chambert-Loir
Antoine

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. Chambert-Loir - Equidistribution theorems in Arakelov geometry and Bogomolov conjecture (part2)
Cours
01:33:45
A. Chambert-Loir - Equidistribution theorems in Arakelov geometry and Bogomolov conjecture (part2)
Chambert-Loir
Antoine

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. Chambert-Loir - Equidistribution theorems in Arakelov geometry and Bogomolov conjecture (part1)
Cours
00:55:14
A. Chambert-Loir - Equidistribution theorems in Arakelov geometry and Bogomolov conjecture (part1)
Chambert-Loir
Antoine

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.

J. Bruinier et J. Ignacio Burgos Gil - Arakelov theory on Shimura varieties (part2)
Cours
01:24:56
J. Bruinier et J. Ignacio Burgos Gil - Arakelov theory on Shimura varieties (part2)
Bruinier
Jan Hendrik
Burgos Gil
José Ignacio

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

J. Bruinier et J. Ignacio Burgos Gil - Arakelov theory on Shimura varieties (part1)
Cours
01:21:08
J. Bruinier et J. Ignacio Burgos Gil - Arakelov theory on Shimura varieties (part1)
Bruinier
Jan Hendrik
Burgos Gil
José Ignacio

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

J-B Bost - Theta series, infinite rank Hermitian vector bundles, Diophantine algebraization (Part2)
Cours
01:26:52
J-B Bost - Theta series, infinite rank Hermitian vector bundles, Diophantine algebraization (Part2)
Bost
Jean-Benoît

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

J-B Bost - Theta series, infinite rank Hermitian vector bundles, Diophantine algebraization (Part1)
Cours
01:31:04
J-B Bost - Theta series, infinite rank Hermitian vector bundles, Diophantine algebraization (Part1)
Bost
Jean-Benoît

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

F. Andreatta - The height of CM points on orthogonal Shimura varieties and Colmez conjecture (part5)
Cours
00:54:52
F. Andreatta - The height of CM points on orthogonal Shimura varieties and Colmez conjecture (part5)
Andreatta
Fabrizio

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

F. Andreatta - The height of CM points on orthogonal Shimura varieties and Colmez conjecture (part4)
Cours
01:33:11
F. Andreatta - The height of CM points on orthogonal Shimura varieties and Colmez conjecture (part4)
Andreatta
Fabrizio

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

F. Andreatta - The height of CM points on orthogonal Shimura varieties and Colmez conjecture (part3)
Cours
01:01:33
F. Andreatta - The height of CM points on orthogonal Shimura varieties and Colmez conjecture (part3)
Andreatta
Fabrizio

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

F. Andreatta - The height of CM points on orthogonal Shimura varieties and Colmez conjecture (part2)
Cours
01:30:56
F. Andreatta - The height of CM points on orthogonal Shimura varieties and Colmez conjecture (part2)
Andreatta
Fabrizio

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

F. Andreatta - The height of CM points on orthogonal Shimura varieties and Colmez conjecture (part1)
Cours
01:02:20
F. Andreatta - The height of CM points on orthogonal Shimura varieties and Colmez conjecture (part1)
Andreatta
Fabrizio

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

Intervenants

France
Professeur de mathématiques à l'Institut de Recherche Mathématique Avancée, Université Louis Pasteur et C.N.R.S., Strasbourg (en 1998), directeur de thèse à l'Université Joseph Fourier de Grenoble, en poste au laboratoire de mathématiques (en 2003). Professeur des Universités à l'Université Joseph Fourier de Grenoble en 2019