Class field theory for curves over local fields

TL;DR

This paper develops a ramified class field theory for smooth projective curves over local fields, introducing new results for 2-dimensional local fields and a duality theorem for logarithmic Hodge-Witt cohomology.

Contribution

It provides the first ramified class field theory for curves over local fields and advances understanding of 2-dimensional local fields and Hodge-Witt cohomology duality.

Findings

New ramified class field theory for curves over local fields

Results on class field theory for 2-dimensional local fields

Duality theorem for logarithmic Hodge-Witt cohomology

Abstract

We establish a ramified class field theory for smooth projective curves over local fields. As key steps in the proof, we obtain new results in the class field theory for 2-dimensional local fields of positive characteristic, and prove a duality theorem for the logarithmic Hodge-Witt cohomology on affine curves over local fields.