A Note on Tamely Ramified Class Field Theory of Two Dimensional Local Rings
Shinji Ishida
TL;DR
This paper explores the tame class field theory for semi-stable two-dimensional local rings, extending prior work on unramified cases to include ramified scenarios.
Contribution
It provides new insights into tame class field theory specifically for semi-stable two-dimensional local rings, a case not previously fully addressed.
Findings
Develops tame class field theory for semi-stable local rings
Builds on Saito's unramified class field theory for two-dimensional rings
Extends understanding of ramified class field theory in this context
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.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Algebraic Geometry and Number Theory · Nonlinear Waves and Solitons