Arithmetic Algebraic Geometry I
The purpose of the course is to give a an introduction to the theory of schemes, which forms the basic language of modern algebraic geometry. The canonical reference for this material is Grothendieck's Élément de géométrie algébrique (EGA). The material covered includes Spec of a ring, Proj of a graded ring, and the notions of proper, smooth, and étale morphisms between schemes. It is the intention that, at the end of the course, participants should have an overview of EGA together with detailed a knowledge of selected passages.
Text: The main text is Grothendieck's EGA which is available from Numdam by following the links below. The text is divided into 5 chapters, beginning with Chapter 0 which contains background material from commutative algebra and homological algebra. Chapters 3 and 4 are published in two and four parts, respectively, and Chapter 0 is published in three parts, at the beginning of EGA I, EGA III 1, and EGA IV 1. It is a good idea to look through the lists of contents, which are located at the end of each installment of the series, to get a sense of the distribution of the material.
A useful shorter text is Mumford's The Red Book of Varieties and Schemes, reprinted as Lecture Notes in Mathematics 1358 from Springer. Chapters II and III, in particular, explain some basic ideas well. A nice short text on (Grothendieck topologies and) sheaves is Artin's Grothendieck Topologies. Another comprehensive source is the Stacks Project.
Lectures: Mondays 9:15-11:00 in Auditorium 6 and on Fridays 9:15-10:00 in Auditorium 7.
Recitations: Mondays 11:15-12:00 and 13:15-15:00 in the seminar room on the fourth floor with Kristian Moi as instructor.
Problems for recitations: