This book is devoted to the proof of a deep theorem in arithmetic geometry, the Fekete-Szegö theorem with local rationality conditions. The prototype for the theorem is Raphael Robinson's theorem on totally real algebraic integers in an interval, which says that if [a,b] is a re…
Abelian varieties with complex multiplication lie at the origins of class field theory, and they play a central role in the contemporary theory of Shimura varieties. They are special in characteristic 0 and ubiquitous over finite fields. This book explores the relationship betwe…
"Extremely carefully written, masterfully thought out, and skillfully arranged introduction ... to the arithmetic of algebraic curves, on the one hand, and to the algebro-geometric aspects of number theory, on the other hand. ... an excellent guide for beginners in arithmetic ge…
A text for a year-long introduction to arithmetic geometry, leading the reader in a logical progression from the local to the global properties of rings and curves through the study of class groups and of the Riemann-Roch theorem. Emphasizes the connection between algebraic numb…
Ce volume est consacré à l'arithmétique p-adique des formes modulaires de Hilbert. Il contient plusieurs théorèmes de classicité de formes surconvergentes généralisant d'une part le critère de Coleman, valable en poids assez grand, d'autre part celui de Buzzard-Taylor, valable e…