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

. We draw concrete consequences from our arithmetic duality for two-dimensional local rings with perfect residue field. These consequences in- clude 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 ear-lier and prove some finiteness properties about them.

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