This chapter reviews the theory of abelian varieties emphasizing those points of particular
interest to arithmetic geometers. In the main it follows Mum-ford’s book [16] except that most …

… JS Milne … Copyright c 1996–2020 JS Milne. Single paper copies for noncommercial
personal use may be made without explicit permission from the copyright holder. … For …

This chapter contains a detailed treatment of Jacobian varieties. Sections 2, 5, and 6 prove
the basic properties of Jacobian varieties starting from the definition in Section 1, while the …

… Copyright c 2004, 2006 JS Milne. The electronic version of this work is licensed under a
Creative Commons License: … abelian varieties (Milne 1986b). Throughout the chapter …

This is an introduction to the theory of Shimura varieties, or, in other words, to the arithmetic
theory of automorphic functions and holomorphic automorphic forms.

L’objet de la théorie du corps de classes est de montrer comment les extensions abéliennes
d’un corps de nombres algébriques K peuvent être déterminées par des éléments tirés de …

… Copyright c 1998, 2008, JS Milne. Single paper copies for noncommercial personal use may
be made without explicit permission from the … Thus 'js.X/ and s are inverse isomorphisms. …

Deligne has expressed the hope that a Shimura variety whose weight is defined over Q is the
moduli variety for a family of motives. Here we prove that this is the case for “most” Shimura …

Human adolescent pregnancy is characterized by poor pregnancy outcome; the risks of
spontaneous miscarriage, prematurity, and low birth weight are particularly acute in girls who …

… In order to provide an accessible introduction to étale cohomology, JS Milne offers this more
… After a detailed analysis of the cohomology of curves and surfaces, Professor Milne proves …