The direct summand conjecture, Spring 2016

Professor A.J. de Jong, Columbia university, Department of Mathematics.

Basic setup: we will work backwards through the recent proof of the direct summand conjecture by Yves Andre. We will follow the proof as reworked in Bhargav's preprint.

Links:

• The original exposition by Andre is here Yves Andre's paper.
• Bhargav's preprint: Bhargav's paper.
• Hochster's home page: Hochster's page.
• Bhargav's home page: Bhargav's page.

Organizational:

1. If you are my graduate student, then please talk to me about attending this seminar.
2. Please email me if you want to be on the associated mailing list.
3. The talks will be 2x45 minutes with a short break.
4. Time and place: Fridays, 10:30 -- 12:00 in Room 407
5. First meeting: Friday, January 27.

List of lectures: TBA

1. Friday, January 27. Speaker: Johan de Jong. Statement and discussion of the direct summand conjecture, proof in characteristic zero, proof in characteristic p. Some discussion of the derived direct summand conjecture.
2. Friday, February 3. Speaker: Johan de Jong. Overview of the proof as in the paper by Bhargav.
3. Friday, February 10. Speaker: David Hansen. Introducing perfectoid spaces and almost mathematics.
4. Friday, February 17. Speaker: Dmitrii Pirozhkov. Almost purity.
5. Friday, February 24. Speaker: Shizhang Li. The almost faithfully flat thingamabob of Yves Andre.
6. Friday, March 3. Speaker: Johan de Jong. Formal schemes, hensel schemes, a thesis problem, and sheafy adic spaces; or, how not to give a seminar talk.
7. Friday, March 10. No talk.
8. Friday, March 17. Spring break.
9. Friday, March 24. No talk.
10. Friday, March 31. Speaker: Shizhang Li, Pro-almost-zero or almost-pro-zero, that is the question
11. Friday, April 5. Speaker: Michael Harris, Counting points on compact Shimura varieties, and the trace formula