On the ramified class field theory of relative curves

TL;DR

This paper extends Deligne's tame geometric class field theory to relative curves with arbitrary ramification, broadening the theoretical framework for understanding class field theory in more complex geometric settings.

Contribution

It introduces a generalized approach to class field theory for relative curves, accommodating arbitrary ramification, which was not covered in previous formulations.

Findings

Generalization of Deligne's approach to relative curves

Inclusion of arbitrary ramification cases

Enhanced understanding of geometric class field theory

Abstract

We generalize Deligne's approach to tame geometric class field theory to the case of a relative curve, with arbitrary ramification.