De Rham epsilon factors for flat connections on higher local fields

TL;DR

This paper develops a formalism for graded epsilon lines associated with flat connections on higher local fields, using advanced algebraic tools like Grayson's binary complexes and $n$-Tate spaces, extending the theory of de Rham epsilon factors.

Contribution

It introduces a new formalism for graded epsilon lines for flat connections on higher local fields, based on comparing Higgs and de Rham complexes.

Findings

Defines graded epsilon lines using binary complexes and $n$-Tate spaces.

Establishes a comparison between Higgs and de Rham complexes.

Extends de Rham epsilon factor theory to higher local fields.

Abstract

This note is a companion to the author's "Higher de Rham epsilon factors". Using Grayson's binary complexes and the formalism of $n$-Tate spaces we develop a formalism of graded epsilon lines, associated to flat connections on a higher local field of characteristic $0$. The definition is based on comparing a Higgs complex with a de Rham complex on the same underlying vector bundle.