Topics in Algebra and Number Theory (MATH596):

A first course in algebraic geometry: the theory of schemes

Lecturer: Prof. Eyal Goren
Location and time: Monday 13:00 - 15:00 in BURN 1214 and Friday 10:00 - 12:00 in BURN 920. Friday 11-12 is designated as an exercise session, except for the first week of classes, where it will a regular lecture hour.

Office Hours: Monday 11:30-12:00 and Friday 12:00-12:30, or by appointment (eyal.goren@mc?ill.ca)

Syllabus: This is an introductory graduate course in algebraic geometry that begins with the theory of schemes from day one. It does not assume any previous familiarity with algebraic geometry. It assumes background in algebra equivalent to the McGill courses MATH 370 and 371 (that is, basic knowledge of rings and modules, fields and Galois theory. Topics such as projective modules, localization, integral extensions and so on, are not assumed.)
The goal of the course is to get a basic understanding of algebraic geometry and an intimate knowledge of some of the key examples and techniques. The text book for this course is Mumford's The red book of varieties and schemes (LNM 1358), with supplements from Eisenbud and Harris The geometry of schemes (GTM 197).
The goal is ambitious and cannot be achieved by going linearly line by line over the text book. The lectures will provide some background in commutative algebra (a good combination is to take this course together with the Higher Algebra MATH 570 course, but this is not a requirement), context and motivation by telling you about classical algebraic geometry, historical context and some of the common applications of the theory we are learning, and would develop examples. This is in contrast with a traditional course where one systematically goes though the definitions and proofs line-by-line.
In addition to 3 hours of lectures per week, there would be an additional exercise session. The participation in the exercise session is mandatory as the grade will be based on participation and a class presentation towards the end of the term.
Pre-requisites: MATH 370 and 371, or equivalent.

Method of Evaluation: Exercise sessions (Participation is mandatory). List of Exercises (typos possible!)

Official stuff:
Academic integrity: McGill University values academic integrity. Therefore, all students must understand the meaning and consequences of cheating, plagiarism and other academic offences under the Code of Student Conduct and Disciplinary Procedures (see www.mcgill.ca/integrity for more information).
Submitting work: In accord with McGill University’s Charter of Students’ Rights, students in this course have the right to submit in English or in French any written work that is to be graded.
Syllabus and Grade Calculation: In the event of extraordinary circumstances beyond the University’s control, the content and/or evaluation scheme in this course is subject to change.