** Date** : 5/2001

**Référence :** IHES/M/01/22

**Résumé, Abstract :**
``Periods" is the generic term used to designate the numbers
arising as integrals of algebraic functions over domains
described by algebraic equations or inequalities with
coefficients in $\Q$. This class of numbers, far larger and
more mysterious than the ring of algebraic numbers, is
nevertheless accessible in the sense that its elements are
constructible and that one at least conjecturally has a
way to verify the equality of any two numbers which have
been expressed as periods. Most of the important constants
of mathematics belong to the class of periods, and these
numbers play a critical role in the theory of differential
equations, in transcendence theory, and in many of the
central conjectures of modern arithmetical algebraic
geometry. The paper gives a survey of some of these
connections, with an emphasis on explicit examples and on
open questions.

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**Nature du texte, text type : **Prépublication

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