Class field theory, Hasse principles and Picard-Brauer duality for two-dimensional local rings

Abstract

We draw concrete consequences from our arithmetic duality for two-dimensional local rings with perfect residue field. These consequences include class field theory, Hasse principles for coverings and $K_{2}$ and a duality between divisor class groups and Brauer groups. To obtain these, we analyze the ind-pro-algebraic group structures on arithmetic cohomology obtained earlier and prove some finiteness properties about them.