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

Takashi Suzuki

Published 2022-10-04Version 1

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 structures of the ind-pro-algebraic groups obtained earlier and prove some finiteness properties about them.