Riemannian geometry has today become a vast and important subject. This new book of
Marcel Berger sets out to introduce readers to most of the living topics of the field and …

Using arithmetic intersection theory, a theory of heights for projective varieties over rings of
algebraic integers is developed. These heights are generalizations of those considered by …

For an arithmetic variety and a positive hermitian line bundle, in this paper, we compute the
leading term of the Hilbert function of the line bundle, show the ampleness of the line …

Mesures et équidistribution sur les espaces de Berkovich Page 1 J. reine angew. Math. 595
(2006), 215—235 DOI 10.1515/CRELLE.2006.049 Journal für die reine und angewandte …

We prove a Hilbert-Samuel type result of arithmetic big line bundles in Arakelov geometry,
which is an analogue of a classical theorem of Siu. An application of this result gives …

We associate to certain filtrations of a graded linear series of a big line bundle a concave
function on its Okounkov body, whose law with respect to the Lebesgue measure describes …

In this paper, we establish a theory of adelic line bundles over quasi-projective varieties over
finitely generated fields. Besides definitions of adelic line bundles, we consider their …

Let X be a smooth projective Berkovich space over a complete discrete valuation field K of
residue characteristic zero, endowed with an ample line bundle L. We introduce a general …

The aim of this paper is to study the modified diagonal cycle in the triple product of a curve
over a global field defined by Gross and Schoen. Our main result is an identity between the …

The present book is a new revised and updated version of “Number Theory I. Introduction to
Number Theory” by Yu. I. Manin and AA Panchishkin, appeared in 1989 in Moscow (VINITI …