18.727: Topics in Algebraic Geometry

This is the home page for the course 18.727 (Topics in Algebraic Geometry), offered at MIT during the fall 2004 semester by Kiran Kedlaya. The topic is "Introduction to Rigid Analytic Geometry". The class now meets Mondays and Fridays 11-12:20 in room 2-151 (this is a change from the original meeting time).

I give out detailed typed lecture notes for each class; they are posted here.


I will be away on Monday, November 8, but I have asked Frank Calegari to fill in with a lecture on p-adic modular forms and what they have to do with rigid analytic geometry.

I am still working on the list of optional topics, but you can see the current draft on the notes page.

I've posted corrections to the first few sets of notes (thanks to Abhinav for sending these); feel free to email me corrections to these or future notes, so I can amend the posted notes accordingly. Thanks!

I added a link to Peter Schneider's Nonarchimedean functional analysis to the notes page. In general, I will post links to web literature there (and not here); suggestions are always welcome.

Those interested in the class may also be interested in my graduate student seminar, STAGE (Seminar on Topics in Arithmetic Geometry, Etc.).

More about the topic

Here is a brief discussion about the course material: [tex, dvi, ps, pdf]. I'd like to explicitly reiterate a point from that discussion: I am willing to tailor the exact topics covered based on audience feedback. (Note: I've relaxed the requirements for a course grade since writing this; see below.)


18.726 or equivalent (e.g., Harvard's Math 260). More explicitly, algebraic geometry in the language of schemes, at the level of Chapters II and III of Hartshorne (i.e., through sheaf cohomology). If you're unsure, contact me and we'll figure out your situation.


I will be distributing typed lecture notes in class and posting them on this web site, so no textbook is required. However, I strongly recommend getting access to the new book Rigid analytic geometry and its applications, by Jean Fresnel and Marius van der Put (Birkhäuser, 2004), which I will be following in large part. (There are one circulating copy and one reserve copy in the MIT library; the Harvard science library also has a copy, as does the Harvard math library.) I will also be making reference to Non-archimedean analysis, by Bosch, Güntzer, and Remmert, but it is unfortunately out of print. I will provide more references as the semester goes along.

How to get a grade (edited version)

If you are a graduate student and have passed your general exam, stop reading; you will not be required to submit anything to receive your grade, though you are encouraged to try the homeworks and/or contribute to the notes. (This is also true if you are not enrolled for the course.) Otherwise, keep reading.

If you are still reading: I will be assigning homework sporadically (but I'll try to keep it about weekly). I originally thought about asking for contributions to the notes, and those are still welcome, but I think I'll just stick to asking for homeworks.

Syllabus/lecture notes

See the notes page for a partial summary of topics to be covered; as the term progresses, it will also be populated with lecture notes.