Ben Antieau : Maximal orders in unramified division algebras

Posted by , part of the Algebraic Geometry Seminar.

At

Aug. 29, 2012, 4 p.m.

In

SEO 427

Abstract

I will describe how to use algebraic topology and representation theory to construct examples of smooth varieties $X$ over the complex numbers and division algebras $D$ over the function field $\mathbb{C}(X)$ such that $D$ is unramified over $X$, and yet there are no projective maximal orders for $D$ over $X$. This solves an old question of Auslander and Goldman, who showed this cannot happen if $X$ is a curve or a surface. Time-permitting, I will discuss the relevance of this research to the period-index problem.