Event
Nathan Grieve, Michigan State University
On the birational geometry of log-pairs determined by Brauer classes via maximal orders
I will report on a joint work with Colin Ingalls in which we use ideas from the minimal model program to define concepts of Iitaka and Kodaira dimensions for Brauer classes.  One of our main goals is to study the behaviour of these  dimensions as  functions of geometric and algebraic parameters.  For instance, we establish a birationally invariant definition of Kodaira dimension for Brauer classes.  Further, we prove that this notion of Kodaira dimension does not decrease under those embeddings of division algebras which induce a Galois extension of their centres. Â