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

This is the authors' abstract. We don't add key points for this paper.

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.