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

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

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

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

Le théorème de Hilbert-Samuel en géométrie algébrique relie le comportement asymptotique du système linéaire gradué d’un faisceau inversible ample au nombre d’intersection. Gillet et Soulé ont

Le théorème de Hilbert-Samuel en géométrie algébrique relie le comportement asymptotique du système linéaire gradué d’un faisceau inversible ample au nombre d’intersection. Gillet et Soulé ont

Le théorème de Hilbert-Samuel en géométrie algébrique relie le comportement asymptotique du système linéaire gradué d’un faisceau inversible ample au nombre d’intersection. Gillet et Soulé ont

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.

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.

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.

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.

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