Periods Page 1 Periods MAXIM KONTSEVICH . DON ZAGIER Introduction As beginning
students of mathematics, we learn successively about various kinds of numbers. First come …

Nous prouvons que tout (ϕ, N)-module filtré faiblement admissible est admissible, ce qui
fournit une description de la catégorie des représentations semi-stables d'un corps local …

Sur quelques représentations modulaires et p -adiques de GL 2 ( Q p ): I Page 1 Sur
quelques repre“sentations modulaires et p-adiques de GL 2 šQpŽ: I šOn Some Modular …

Let M be the Shimura variety associated with the group of spinor similitudes of a quadratic
space over Q of signature (n,2). We prove a conjecture of Bruinier-Kudla-Yang, relating the …

We give a proof of the André-Oort conjecture for A_g---the moduli space of principally
polarized abelian varieties. In particular, we show that a recently proven``averaged" version …

Nous conjecturons que la réduction modulo des représentations cristallines irréductibles de
dimension 2 sur peut être prédite par la réduction modulo. Nous explicitons quelques …

In Fall 2003, Jean-Marc Fontaine was appointed as Chair Professor of Arithmetic Geometry
at Tsinghua University in Beijing. This was the starting point of broad Sino-French …

The Colmez conjecture is a formula expressing the Faltings height of an abelian variety with
complex multiplication in terms of some linear combination of logarithmic derivatives of Artin …

We study the Faltings height pairing of arithmetic special divisors and CM cycles on Shimura
varieties associated to orthogonal groups. We compute the Archimedean contribution to the …

The present book is a new revised and updated version of “Number Theory I. Introduction to
Number Theory” by Yu. I. Manin and AA Panchishkin, appeared in 1989 in Moscow (VINITI …