Tame class field theory over local fields

2022/09/07 by Rahul Gupta, Gupta, Rahul, Amalendu Krishna +3 · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Advanced Differential Equations and Dynamical Systems #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2209.02953

Abstract

For a quasi-projective scheme X admitting a smooth compactification over a local field of residue characteristic p > 0, we construct a continuous reciprocity homomorphism from a tame class group to the abelian tame etale fundamental group of X. We describe the prime-to-p parts of its kernel and cokernel. This generalizes the higher dimensional unramified class field theory over local fields by Jannsen-Saito and Forre. We also prove a finiteness theorem for the geometric part of the abelian tame etale fundamental group, generalizing the results of Grothendieck and Yoshida for the unramified fundamental group.

Cited by

• Zero-cycles on quasi-projective surfaces over p-adic fields

Related

• Tame Class Field Theory for Singular Varieties over Algebraically Closed Fields
• Finite presentation of the tame fundamental group
• Class field theory for open curves over local fields
• Two-Dimensional Local-Global Class Field Theory in Positive Characteristic
• Covering data and higher dimensional global class field theory