Explicit local reciprocity for tame extensions

2010/01/13 by Rachel Newton, Newton, Rachel · 1 citation
Mathematics · #11A15 #11F85 (Primary) #16K50 (Secondary) #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1001.2233

openalex publication_date 2010/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider a tamely ramified abelian extension of local fields of degree n, without assuming the presence of the nth roots of unity in the base field. We give an explicit formula which computes the local reciprocity map in this situation.

Cited by

• Machines Learn Number Fields, But How? The Case of Galois Groups

Related

• Fesenko reciprocity map
• Ramification theory of reciprocity sheaves, II, Higher local symbols
• Tame class field theory over local fields
• Diophantine geometry and non-abelian reciprocity laws I
• Reciprocity Laws for the Higher Tame Symbol and the Witt Symbol on an\n Algebraic Surface