Apparaît dans les collections : Algèbre, Géométrie et Physique : une conférence en l'honneur, Fields medallists - 1982

We show that the non-commutative geometric approach to the Riemann zeta function has an algebraic geometric incarnation: the «Arithmetic Site». This site involves the tropical semiring viewed as a sheaf on the topos dual to the multiplicative semigroup of positive integers. We realize the Frobenius correspondences in the square of the «Arithmetic Site».