Locally convex structures on higher local fields

TL;DR

This paper explores the locally convex topological structures of higher local fields, extending previous two-dimensional results, and investigates their duality and submodule properties.

Contribution

It generalizes the description of higher local fields as locally convex vector spaces and establishes duality and submodule properties in this broader context.

Findings

Higher local fields can be described as locally convex vector spaces with fixed embeddings.

Bounded and compactoid submodules are characterized within these fields.

A self-duality result is established with an appropriate dual topology.

Abstract

We establish how a higher local field can be described as a locally convex vector space once an embedding of a local field into it has been fixed. This extends previous results that had been obtained in the two-dimensional case. In particular, we study bounded and compactoid submodules of these fields and establish a self-duality result once a suitable topology on the dual space has been introduced.