Majorations explicites de fonctions de Hilbert-Samuel g\'eom\'etrique et   arithm\'etique
  By using the $\mathbb R$-filtration approach of Arakelov geometry, one establishes explicit upper bounds for geometric and arithmetic Hilbert-Samuel function for line bundles on projective varieties and hermitian line bundles on arithmetic projective varieties. 
Huayi Chen (IF)
math.AG math.NT