The Grothendieck ring of varieties and cancellation property for orders in a quaternion algebra

Thời gian: 16:30, thứ năm, 29/06/2023

Tóm tắt: A fundamental question about the Grothendieck ring of algebraic varieties is the following: whether two algebraic k-varieties with the same class in K_0(Var_k) are piecewise isomorphic. Using reduction to Krull-Schmidt categories, we reduce the above question for abelian varieties to the following cancellation problem: If we have an isomorphism Ooplus N cong M oplus N where M, N are finitely generated O-modules, and O is an order in a quaternion algebra, can we cancel out N. In this talk, I will explain a strategy to solve this problem.

Hình thức: Offline tại phòng 612 A6 và online qua google meet, cụ thể https://meet.google.com/yep-kbzk-eao?pli=1&authuser=1