M / 911

Let F be a field, D be a central division F-algebra of prime power degree. By the Rost kernel of D we mean the subgroup of F^* consisting of elements \lambda such that the cohomology class (D)\cup (\lambda)\in H^3(F) vanishes. In general, this subgroup contains the Suslin kernel, which we define to be the group generated by m-th powers of reduced norms from D^{\otimes m}, for all m\ge 1. In 1985, Suslin conjectured that the Rost and the Suslin kernels always coincide. In this talk we will discuss some new cases of his conjecture, for complete discrete valuation fields. This is based on a joint work with Zhengyao Wu.

Yong Hu

Southern University of Science and Technology, Shenzhen, China