189-571B: Higher Algebra II

Professor: Henri Darmon
Classes: MWF 8:30-9:30.
Room: Burnside Hall 920

Higher Algebra II on the web:
Henri Darmon's web page: http://www.math.mcgill.ca/~darmon
Math 571B: http://www.math.mcgill.ca/~darmon/courses/algebra2/algebra2.html

Office hours:
Henri Darmon: Feel free to drop by my office (room 1111) at any time. To be sure to catch me you can make an appointment with me by email.

Contents of the course:
The content and pace will build on the concepts you have acquired in Eyal Goren's course in the first semester. In particular, some familiarity and ease with the language of category theory, and some rudimentary familiarity with schemes, will be assumed.
As in the first semester, emphasis will be placed on rigorous proofs, and on developping mathematical maturity and problem-solving skills. We will be covering the following topics, using references that are available on-line and can be dowloaded for free onto your electronic devices.

A. Dedekind rings and unique factorisation.
Reference: Milne's Algebraic Number Theory, Chapters 1, 2, and 3.

B. Introduction to commutative algebra and algebraic geometry.
Reference: Ernst Kunz's Introduction to Commutative Algebra and Algebraic Geometry, Chapters 1-4.

C. Wedderburn-Artin theory of (non-commutative) semisimple algebras, the Brauer group.
Reference: Anthony Knapp's Advanced Algebra, Chapters 2 and 3.

Course blog: A more detailed, weekly log of what has been covered in the class will be maintained in the course blog.

Grading Scheme :

20% Weekly assignments. I will be posting assignment every two weeks. These assignments will be due on a Wednesday and returned to you on the Friday of the same week.

20% One-hour in-class midterm.

60% Three-hour in-class Final.

There will be an option of 80% final + 20% assignments if you score better on the final than on the midterm.

The obligatory statements

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).

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.

In the event of extraordinary circumstances beyond the University's control, the content and/or evaluation scheme in this course is subject to change.