Tame Class Field Theory for Singular Varieties over Finite Fields

TL;DR

This paper extends the description of the abelian tame fundamental group from smooth to singular varieties over finite fields by utilizing Weil-Suslin homology, broadening the scope of class field theory in algebraic geometry.

Contribution

It generalizes Schmidt and Spie{ extss}’s result to singular varieties by replacing Suslin homology with Weil-Suslin homology, enabling the study of more complex algebraic structures.

Findings

Generalization of tame fundamental group description to singular varieties

Use of Weil-Suslin homology in class field theory

Broader applicability to algebraic geometry over finite fields

Abstract

Schmidt and Spie{\ss} described the abelian tame fundamental group of a smooth variety over a finite field by using Suslin homology. In this paper we show that their result generalizes to singular varieties if one uses Weil-Suslin homology instead.