Twisted Class Field Theory

2015/06/17 by Yoon, Seok Ho Jack
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1506.05365

Abstract

Neukirch has developed explicit and axiomatic class field theory, which applies to both local and global fields. One of the key ingredients in his theory is a ℤ-extension of the base field, and in the case of ℚ_p, he uses the maximal unramified extension. However ℚ_p has another ℤ-extension, which we shall denote by ℚ_p. Thus, it is natural to ask if we could verify all the axioms required by taking ℚ_p as the central object instead. We prove this is possible and the two reciprocity maps induced from the two distinct ℤ-extensions are the same.

Related

• Neukirch's Approach to the Reciprocity Map and Global Class Field theory in Positive Characteristic
• Derived class field theory
• Two-Dimensional Local-Global Class Field Theory in Positive Characteristic
• Class field theory for products of open curves over a local field
• Class field theory for open curves over local fields, II