Math 274 - Rational points on varieties

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Course notes (.pdf) (.dvi.gz) (these are continually under construction - last revision 4/28/03)

Homework 1 and solutions (.pdf) (.dvi.gz)
Homework 2 and solutions (.pdf) (.dvi.gz)
Homework 3 and solutions (.pdf) (.dvi.gz)
Homework 4 and solutions (.pdf) (.dvi.gz)
Homework 5 and solutions (.pdf) (.dvi.gz)
Homework 6 and solutions (.pdf) (.dvi.gz)
Homework 7 and solutions (.pdf) (.dvi.gz)
Homework 8 and solutions (.pdf) (.dvi.gz)
Homework 9 and solutions (.pdf) (.dvi.gz)
Homework 10 and solutions (.pdf) (.dvi.gz)
Homework 11 and solutions (.pdf) (.dvi.gz)

Instructor: Bjorn Poonen

Lectures: MWF 10-11am in 51 Evans

Course Control Number: 55146

Office: 703 Evans, e-mail: poonen@math

Office Hours: Wed, Fri 11:10-12 or by appointment.

Prerequisites: Algebraic number theory (254A is enough), algebraic geometry (256AB - e.g. Hartshorne's book, the more the better), and some group cohomology (e.g., Chapter 2 of Milne's course notes on class field theory, available from his website, or Chapters IV (sections 1-8) and V in Cassels and Frohlich, Algebraic number theory).

Syllabus: The course will use the language of schemes to study varieties over fields that are not algebraically closed, and in particular to understand their rational points. Topics will include some subset of the following:

Instead of working toward the proof of one or two big theorems, the goal will be to develop techniques that have wide application in arithmetic geometry.

Required Text: None

Recommended Reading: Notes will be available online. Also, the following books have been put on reserve at the Berkeley math library:

We're not going to cover everything in these books! There are also Milne's course notes on various subjects: the notes on class field theory and etale cohomology are the most relevant to this course.

Grading: There will be no exams. Grades will be based on weekly homework.

Homework: Assignments will be due in class in Mondays. The first one will be due February 3. Late homeworks will not be accepted. You are free to consult any sources (animate or inanimate) while doing your homework, but if you use anything (or anyone) other than your class notes or the texts listed above, you should say so on your homework. Staple loose sheets!!!