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.

Accepted for publication in Algebraic Geometry. No changes in the text from v3. 48 pages

References in corpus (3)

• Duality for cohomology of curves with coefficients in abelian varieties
• Tate Duality In Positive Dimension Over Function Fields
• Finite generation of nilpotent quotients of fundamental groups of punctured spectra