MATH Seminar

Title: Ramification in bad characteristics
Seminar: Algebra
Speaker: David Saltman of Center for Communications Research, Princeton
Contact: R. Parimala, parimala@mathcs.emory.edu
Date: 2009-04-07 at 4:00PM
Venue: MSC W303
Download Flyer
Abstract: Let $C$ be a curve over a $p-$adic field $F$ and $K = F(C)$. For division algebras of exponent prime to $p$, it is known that index divides the square of the exponent and division algebras of prime degree are cyclic. Both results avoid the prime $p$ because in that case there is no good theory of ramification of Brauer group elements. However, one can try and avoid this obstacle by defining the ramification group of a discrete valued field $K$ with valuation ring $R$ as the quotient of Brauer groups $Br(K)/Br(R)$ and then study the functorial properties of this quotient. One is then led to the complete case and to consider the paper ``A generalization of local class field theory by using K groups I'' by Kazuya Kato (J Fac Sci Sec. IA 26, 2 303-376). We will discuss the progress we have made on this problem using Kato's work.