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.