F. Andreatta - The height of CM points on orthogonal Shimura varieties and Colmez conjecture (part5)

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

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

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

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

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

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

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

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

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.

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

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

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.