I'd like to revive the student reading seminar in algebraic geometry
from last year -- I was thinking about having a classics reading course. Below I've written out a tentative schedule.
Here's how I envision the layout of the seminar. We'd spend about a month on each paper (plus or minus one or two weeks, depending on the paper and the interests of the participants). About a month before we begin talking about each paper, we'd assign speakers, who would read the paper and relevant background; two weeks before we begin, the speakers would meet to discuss the organization of their talks and split up the material.
The first talk for each paper should be understandable *essentially in its entirety* by a student comfortable with Hartshorne I-III and the material covered in the algebra quals (as well as perhaps an average background in algebraic topology and complex analysis). The rest of the talks on each paper should be at least *broadly understandable* to a student with that minimal background, and should not punt anything that is not at the level of a challenging homework exercise. In particular, first-years with a background in algebraic geometry or algebraic number theory should be able to attend this seminar without being intimidated.
Let me know if you have complaints or suggestions about the papers--I'm happy to revise the schedule if there's interest in covering different things. Also let me know if you're interested in participating in (some or most of) the seminar.
-Talk 1 would state the theorem, derive some consequences (e.g. Riemann-Roch for curves and surfaces), and give a sketch of the proof ideas (e.g. from Bott's MR)
-Talks 2 and 3 (and possibly 4) would give the proof in some detail
(Daniel Litt, John Pardon)
-Talks 1 would introduce the problem and give background on other classifications of vector bundles (e.g. Grothendieck's theorem about vector bundles on P^1 and Horrock's splitting criterion)
-Talk 2-3 would carefully go through the paper
(Sam Lichtenstein, Rebecca Bellovin)
-Talk 1 would give preliminaries on central simple algebras, Brauer groups of fields, Skolem-Noether, and describe the Brauer group of finite CW complexes (that is, the first half or so of Le Groupe de Brauer I + background)
-Talk 2 would discuss the situation over a general (Noetherian) base and describe interpretations in terms of Azumaya algebras, Severi-Brauer varieties, etc. (with examples)
-Talks 3 and 4 would be up to the speakers
-Talks 1 and 2 would go through the paper in some detail
-Talk 3 would make the language of stacks more explicit than Mumford does; a good reference is Jonathan Wang's
senior thesis, as well as FGA Explained III-IV
-Talk 4 would study some examples of algebraic stacks; e.g. BG and M_{1,1} again
-Talk 1 would discuss the Hodge decomposition, degeneration of the Hodge-to-de Rham spectral sequence, and the Kodaira et al vanishing theorem. Ideally it would include a (necessarily very brief) review of the analytic arguments for these results
-Talk 2 would discuss the algebraic-to-analytic de Rham comparison theorem, following Grothendieck's short paper
here -Talks 3-5 would go through the Deligne/Illusie paper in some detail
-Talk 1 would discuss the problem, and prove unirationality of a cubic threefold (as in
these notes)
-Talk 2 would give background on intermediate Jacobians and deformations of cycles (following Voisin's Hodge Theory)
-Talks 3-4 (and possibly 5) would go through the actual material in Clemens/Griffiths
-- Tate, Finite Flat Group Schemes (in Modular Forms and Fermat's last theorem)
-Talk 1 would be definitions and lots of examples
-Talks 2-4 would just follow Tate somewhat slavishly
This page is maintained by Daniel Litt and was shamelessly copied from Rebecca Bellovin's page, in the last of a long chain of webpage thefts.