Locally convex structures on higher local fields

2012/10/30 by Alberto Camara, Camara, Alberto
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Functional Analysis (math.FA) #Number Theory (math.NT) #math.AG #math.FA #math.NT

paper · pdf · doi:10.48550/arxiv.1210.8068

18 pages

arxiv created 2013/01/31 · arxiv updated 2013/02/01

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.

Related

• Functional analysis on two-dimensional local fields
• Invitation to higher local fields, Part I, section 1: Higher dimensional local fields
• Hahn--Banach Theorem and Duality Theory on non-Archimedean Locally Convex Spaces
• Invitation to higher local fields, Part I, section 10: Explicit higher local class field theory
• Invitation to higher local fields, Part II, section 8: Higher local skew fields