Symbol length in the Brauer group of a field

Sun, 15/11/2015 - 12:00
The Merkurjev-Suslin Theorem tell us that the n-torsion part of the Brauer group of a field containing a primitive n-th root of 1 is generated by symbol algebras. A natural question is:What can be said on the minimal number of symbols needed.
In this talk I will survey some of the known results and give the idea for the proof for a bound in a geometric situation (by which I mean when the base field contains an algebraically closed field).