Around the descent conjecture
Người báo cáo: Nguyễn Mạnh Linh
Thời gian: 16h30 thứ năm, ngày 8/06/2023
Địa điểm: Pòng 612, Nhà A6.
Link online: https://meet.google.com/yep-kbzk-eao?pli=1&authuser=4
Tóm tắt: The descent method is one of the strategies allowing one to study the Brauer–Manin obstruction to the local-global principle and to weak approximation on varieties over number fields, by reducing the problem to "descent varieties". Very recently in his Park City lecture notes, Wittenberg formulated a "descent conjecture" for torsors under linear algebraic groups. The present article gives a proof of this conjecture in the case of connected groups, generalizing the toric case from the previous work of Harpaz–Wittenberg. As an application, we deduce directly from Sansuc's work the theorem of Borovoi on Brauer–Manin obstruction for homogeneous spaces of connected linear algebraic groups with connected stabilizers. We are also able to reduce the general case to the case of finite (étale) torsors. Another innovation is the notion of non-abelian descent types, which generalizes (and which is more accessible than) that of extended type of torsors under groups of multiplicative type by Harari–Skorobogatov.
Reference: https://arxiv.org/abs/2305.13228
