Back to Goren's homepage

# 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.