A Note on Tamely Ramified Class Field Theory of Two Dimensional Local Rings

2022/04/24 by Ishida, Shinji
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2204.12286

Abstract

In this note, we treat two dimensional complete local rings which are called "semi-stable local rings" and discuss the tame class filed theory. In 1987, Professor S. Saito completed the unramified class field theory of the general two dimensional excellent local rings. On the other hand, we discuss the tame class field theory for a specific local rings.

Related

• Two-Dimensional Local-Global Class Field Theory in Positive Characteristic
• Tame class field theory over local fields
• Invitation to higher local fields, Part I, section 16: Higher class field theory without using K-groups
• Class Field Theory and Arithmetic of Abelian Varieties over Local Fields
• ℓ-adic class field theory for regular local rings