The definition of “building”, to be given in the first section below, involves three axioms which
are quite easy to state. It is not so easy, however, to motivate this definition. In particular, you …

Abstract CONTENTS Introduction § 1. Complexes of curves and families of functions § 2.
Singularities and non-degeneracy of functions § 3. Some variants of the complex of curves § …

We describe recent work of Klyachko, Totaro, Knutson, and Tao that characterizes
eigenvalues of sums of Hermitian matrices and decomposition of tensor products of …

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 …

Symmetric and locally symmetric spaces arise in different contexts. Many natural spaces of
this type are not compact and, for many applications, it is necessary to compactify them. This …

In these lecture notes we give an introduction to Bridgeland stability conditions on smooth
complex projective varieties with a particular focus on the case of surfaces. This includes …

We prove the Fargues-Rapoport conjecture for p-adic period domains: for a reductive group
G over a p-adic field and a minuscule cocharacter {\mu} of G, the weakly admissible locus …

A Reverse Minkowski Theorem Page 1 A Reverse Minkowski Theorem Oded Regev ∗
Courant Institute, New York University New York, New York 10012, United States Noah …

1.1. Certains problèmes géométriques ou arithmétiques se ramènent parfois à décider si
une fonction analytique, voire une série formelle, est en fait une fonction algébrique, voire …

The purpose of this book is to build the fundament of an Arakelov theory over adelic curves
in order to provide a unified framework for the researches on arithmetic geometry in several …