Time：15:00-16:00, December 18 2025
Venue：E14-212
Speaker：Yong Hu，Southern University of Science and Technology
Title：Brauer--Manin obstruction for isometries with prescribed characteristic polynomial
Abstract：For any non-degenerate quadratic space V over K, the characteristic polynomial of any isometry of V is reciprocal. Since an influential paper of Milnor in 1969, it has been an interesting question to determine which quadratic spaces admit an isometry with prescribed characteristic polynomial. When K is a number field, one may also ask for an integral analogue. In the last decade, important progress on these questions has been made by Bayer--Fluckiger and her coauthors. Their method is almost purely algebraic in nature and appears to be somewhat ad hoc. We take an arithmetic geometric viewpoint, and recover their results within the general framework of Brauer--Manin obstruction theory for rational and integral points on homogeneous varieties. This is based on a joint work in progress with Yang Cao, Ting-Yu Lee and Fei Xu.
