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.