In some ways, this course is a language class: we will be learning how to read, write and speak the language of schemes. Along the way, we will absorb some of Grothendieck's insights into this language: the importance of working locally, the relevance of relative properties of morphisms, base change, and how to think algebraically about the cohomology of algebro-geometric objects.

Mondays, Wednesdays, and Fridays, 10-11, room 2-102. I will follow the MIT convention of starting my lectures 5 minutes after the posted start time, and ending them 5 minutes before the posted end time.

Recommended: download Éléments de Géométrie Algébrique, by Grothendieck and Dieudonné, from NUMDAM, and keep it on hand in case you need to look up one of the odd references to it I will be sprinkling throughout the course. (See the main web page for precise links.) However, do not attempt to read EGA directly; this has been likened to reading a dictionary, with similarly unfruitful results. On the other end of the intuitive-to-formal spectrum, you may also find helpful The Geometry of Schemes, by Eisenbud and Harris; it provides some intuition lacking in Hartshorne (e.g., the functor of points). Other possible references include Mumford's The Red Book of Varieties and Schemes and Ueno's Algebraic Geometry (all three volumes).

On top of all that, I am planning to distributed typed lecture notes.

Recommended: some exposure to homological algebra (e.g., in 18.905) and rudimentary category theory (as in 18.725 last semester, or 18.905). I'll introduce what I need as I go along, but possibly in a pretty sketchy way with a lot of assertions left as "exercises for the listener".

If you need to turn in a problem set late, please arrange an extension with me beforehand. If you get too far behind, I may ask you to drop the course.

Note that if you intend to submit homeworks for grading, you must be enrolled in the class unless that is impossible (e.g., if you are not a student, or are enrolled at a school that does not permit cross-registration at MIT). This is needed to ensure accurate enrollment figures so that we can be assigned a course grader. If you do not intend to submit homeworks for grading, you may register (or cross-register) as a listener.

If you are an undergraduate (at MIT or elsewhere) wishing to take the course for a grade, please send me an email with a detailed description of the background which you think makes you prepared to take the course. I may ask you to meet me in person to evaluate further.