Title: The period-index conjecture for division algebras
Speaker: Ben Antieau
Speaker Info: University of Illinois Chicago
Brief Description:
Special Note:
Abstract:
I will describe one of the major outstanding problems about division algebras over fields, the period-index problem, as well as its expected solution, the period-index conjecture. The problem is to relate the size of a division algebra measured by its dimension as a vector space to its order in the Brauer group. Classical algebraists such as Wedderburn and Noether set the stage for the study of division algebras and the first major results in the period-index direction are Wedderburn's theorem that finite division algebras are commutative and the Albert--Brauer--Hasse--Noether theorem on division algebras over number fields. In most cases of interest, such as function fields of higher dimensional varieties over the complex numbers or over finite fields, the conjecture is completely open. My own work with Ben Williams poses a topological version of this theorem and, in many cases, answers it, leading to new perspectives on the original problem.Date: Thursday, January 23, 2020