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arXiv · 2210.01396

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

Takashi Suzuki
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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.

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Takashi Suzuki. 2022-10-04. Class field theory, Hasse principles and Picard-Brauer duality for two-dimensional local rings. https://doi.org/10.14231/ag-2024-015

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