Two-Dimensional Local-Global Class Field Theory in Positive Characteristic

2014/03/26 by Kirsty Syder, Syder, Kirsty
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1403.6747

openalex publication_date 2014/03/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using the higher tame symbol and Kawada and Satake's Witt vector method, A. N. Parshin developed class field theory for higher local fields, defining reciprocity maps separately for the tamely ramified and wildly ramified cases. We extend this technique to the case of local-global fields associated to points and curves on an algebraic surface over a finite field.

Citations

• Simple proofs of classical explicit reciprocity laws on curves using determinant groupoids over an artinian local ring

Related

• Class field theory for curves over local fields
• Neukirch's Approach to the Reciprocity Map and 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
• Class field theory for open curves over local fields, II