Differentiability of the arithmetic volume function

Huayi Chen (1)

1 IMJ - Institut de Mathématiques de Jussieu

We introduce the positive intersection product in Arakelov geometry and prove that the arithmetic volume function is continuously differentiable. As applications, we compute the distribution function of the asymptotic measure of a Hermitian line bundle and several other arithmetic invariants.

Domaines: Géométrie algébrique [math.AG]; Théorie des nombres [math.NT]

Huayi Chen. Differentiability of the arithmetic volume function. 2008. ⟨hal-00347405v3⟩