Summer school in commutative algebra:
Local cohomology and its interactions with algebra, geometry,
for graduate students
Monday June 20 -- Thursday June 30, 2005 in
The lecture notes have been rewritten and are
now open for inspection.
Here is the current version. You are invited to give us comments
regarding omissions, repetitions, and errors of all sorts. Please
send them to Uli at email@example.com, regardless of the author
of the chapter in question. Of course, the sooner you send in
corrections/comments, the earlier that we can address them. (Time is
relevant since the notes will be published by the AMS.)
Thanks so much!
(Georgia Tech, firstname.lastname@example.org)
We wish to express our THANKS to
Wayne Drady and the AMS
for all their HELP and SUPPORT, and to
MSRI at Berkeley for the much
appreciated COSPONSORSHIP of this summer school.
This is one of the 2005 Joint Summer Research
Conferences. (Look here for a lot of useful info about these
conferences, and Snowbird in general.)
This summer school is intended for graduate
students only. The application deadline
has passed. Invitation letters for successful
applicants should have arrived.
This page is
Please send questions/remarks to
email@example.com -- but be patient...
Please note that Snowbird is not at sea level. If you have asthma or
altitude sickness you might need to bring medication.
Here is a short script
that gives an introduction to the theory of injective
modules. These are important theoretical
gadgets for the summer school and the properties and results discussed
in the script are yoused throughout the summer school. Injective modules are
covered in most courses on commutative algebra, but we realize that
you may not have had such course. We expect you to have read the script
before you come to Snowbird!
The topic of the summer school will be commutative algebra, with
special emphasis on topics that are related to local cohomology and
its interactions with other areas of mathematics such as algebraic
geometry, topology, and D-modules. Some part of the workshop will be
devoted to algorithmic questions and explicit computations.
Lecture notes for the first part will be developed by the speakers and
they will be distributed before the start of the summer school.
We will have 7 days of lectures, followed by a conference during the
last 3 days. During the lecture period, there will be 3 to 4 one hour
classes per day, supplemented by problem sessions, computer demos, and
discussions. These lectures, demos and sessions will be delivered by
Srikanth Iyengar, University of Nebraska
Graham Leuschke, Syracuse University
Anton Leykin, UI at Chicago
Claudia Miller, Syracuse University
Ezra Miller, University of Minnesota
and the organizers.
The speakers for the conference that makes the second part of the
Summer School are expected to be
Markus Brodmann, Universitaet Zuerich
Ragnar-Olaf Buchweitz, University of Toronto
Phillippe Gimenez, Universidad de Valladolid
Gennady Lyubeznik, University of Minnesota
Paul Roberts, University of Utah
Peter Schenzel, Universitaet Halle
Rodney Sharp, University of Sheffield
Ngo Viet Trung, Institute of Mathematics, Hanoi
Keiichi Watanabe, Nihon University
Santiago Zarzuela, Universitat de Barcelona
The talks in this final part are intended to be expository and
centered around the main themes of the summer school.
There will be one day of rest, June 25. We will have an excursion that
Here is the schedule
for the summer school with a rough outline of the
Travel and Lodging
Travel is most easily done through Salt Lake City, which is about 30
miles from Snowbird. The accomodations are entirely provided by the
AMS, including the meals. As stated above, we will cover these
expenses for the students. Rooms will be double occupancy. If you have
someone in mind that you want as roommate, please point this out to
The target population consists of graduate students in their early
years, similar to the Barcelona summer school in 1996. The workshop
will be designed to accommodate 30 to 40 graduate students
All persons who are interested in participating in one of the
conferences should request an invitation by sending the following
Summer Research Conferences Coordinator,
AMS, P.O. Box 6887,
Providence, RI 02940,
or by email to Wayne Drady at firstname.lastname@example.org no later than
March 3, 2005.
Please type or print the following:
1. Title and dates of conference. (See above.)
2. Full name.
3. Mailing address.
4. Phone numbers (including area code) for office, home, and fax.
5. Email address.
6. Your anticipated arrival/departure dates. (June 19 and July 1.)
7. Scientific background relevant to the conference topics; please
indicate your student status, whether you have an advisor, and why you
are interested in the conference.
8. The amount of financial assistance requested (or indicate if no
support is required).
9. If you are a student at a sponsoring institution of the Mathematics
Sciences Research Institute (MSRI) at Berkeley, please says so very
explicitly in the application (to find out, ask your department chair).
We expect to cover the lodging and the
food at Snowbird for all students.
We may be able to cover some travel expenses. This
will depend on luck.
The following comprises a list of words that will be used often during
the talks. Attendants should be familiar with their meaning.
* ring, homomorphism, prime ideal, maximal ideal, field, zerodivisor,
radical, associated primes of ideals and modules, what are
* topological space, topology, open and closed sets, subspace
topology, continuity (in the general case when no metric is present),
discrete spaces, manifolds, (co)homology
* (additive/linear) functor, category, morphism, natural
transformation, complex of objects in a category, homology,