Brauer Groups, Fall 2011

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

Organizational: The talks will be 2x45 minutes with a short break. Time and place: Fridays 10:30 AM in Room 312.

List of Talks: The talks with lecturer Johan de Jong can still be claimed by graduate students. Let me knowm if you are interesting in giving one of these talks. Another possibility is to "team up" with one of the speakers and give a joint presentation.

nr Date Description Lecturer
0 Sept 9 Organizational Johan de Jong
1 Sept 16 Brauer groups of fields. Following Serre's lectures in the seminar Cartan 1950/51 Andrew Kiluk
2 Sept 23 Brauer groups of fields and Galois cohomology and a bit about cohomological dimension of fields? Tsen's theorem? Rahul Krishna and Ioan Filip
3 Sept 30 A bit about Etale cohomology? Raju Krishnamoorthy
4 Oct 7 Groupes de Brauer I (article by Grothendieck in Dix Exposes sur la cohomologie des schemas) Zachary Maddock and Ashwin Deopurkar
5 Oct 14 Groupes de Brauer II (article by Grothendieck in Dix Exposes sur la cohomologie des schemas) Xia Jie
6 Oct 21 Groupes de Brauer III (article by Grothendieck in Dix Exposes sur la cohomologie des schemas) Johan de Jong
7 Oct 28 Hoobler, Raymond T. When is Br(X)=Br'(X)? Beautiful exposition of Gabber's result which implies that Br(X) = Br'(X) for affine schemes X Frank Gounelas
8 Nov 4 Discussion of various topics: Br(X) = Br'(X) for quasi-projective schemes X, Tate's paper on Brauer groups and K_2 of number fields, Merkurjev-Suslin relating K_2 and the Brauer group of a field. Johan de Jong
9 Nov 11 Brauer groups and quotient stacks. Paper by DAN EDIDIN, BRENDAN HASSETT, ANDREW KRESCH, AND ANGELO VISTOLI relating the question Br = Br' to global quotient stacks Maksym Fedorchuk
10 Nov 18 Brauer-Manin obstruction to existence of rational points Daniel Disegni
11 Dec 2 A.J. de Jong, The period-index problem for the Brauer group of an algebraic surface, Duke Mathematical Journal, 123, 71--94 (2004). Can also do this with the method found by Max Lieblich and this may be more suitable for the seminar Xue Hang
12 Dec 9 Birational invariance of the unramified Brauer group. Artin-Mumford's example of a unirational but not rational variety over an algebraically closed field Xuanyu Pan