MATH Seminar

Title: Tensor products of division algebras
Seminar: Algebra and Number Theory
Speaker: David J. Saltman of CCR Princeton
Contact: Skip Garibaldi, skip@mathcs.emory.edu
Date: 2011-10-25 at 4:00PM
Venue: MSC E406
Download Flyer
Abstract: If $F$ is algebraically closed, and $F_i \supset F$ are field extensions, then $F_1 \otimes_F F_2$ is always a domain. It thus makes sense to conjecture that if $D_i/F_i$ are division algebras (meaning $F_i$ is the center of $D_i$ and $D_i/F_i$ is finite dimensional), then $D_1 \otimes_F D_2$ is a (noncommutative) domain. We will show that this is often true, but not always. We will concentrate on the case that $F$ has characteristic 0 and that the $D_i/F_i$ have prime degree. We also hope to draw attention to the interesting properties of $F_1 \otimes_F F_2$ and how they relate to our problem. Along the way we will make use of Picard varieties and elliptic curves.