## MATH 715, FALL 2002

## COMMUTATIVE ALGEBRA SEMINAR, WINTER 2003

## TIGHT CLOSURE MATERIAL

**
**

Note: The lecture materials are in reverse chronological order.
(The lectures from Fall, 2002 were given
in Math 715. The lectures from Winter, 2003 were given
in the Commutative Algebra Seminar.)

This is a preliminary version of these lecture notes and should
not be used as a reference.

Lectures of April 24 and 25

Lecture of April 22

Lecture of April 17

Lecture of April 10

Lecture of April 3

Lecture of March 6

Lecture of February 20

Lecture of February 13

Lecture of February 6

Lecture of January 30

Lecture of January 23

Lecture of January 16

Lecture of January 9

Preliminary written version of three lectures on tight closure
given during the Introductory Workshop for the year in Commutative Algebra
at MSRI, September 9, 10, and 11, 2002:

Tight closure theory and characteristic
*p* methods.

This write-up covers most of the material discussed in
the first several lectures of the course.

Problem sets:
1 *
2 *
3 *
4 *
5

Solutions: 1
* 2
* 3