Pontryagin duality for varieties over $p$-adic fields

TL;DR

This paper develops a duality theory for varieties over p-adic fields using cohomological complexes of locally compact abelian groups, establishing a Pontryagin duality between motivic cohomology groups.

Contribution

It introduces a new duality framework for motivic cohomology over p-adic fields based on Pontryagin duality, under specific assumptions.

Findings

Established a duality theorem for cohomological complexes

Defined locally compact motivic cohomology groups

Proved Pontryagin duality between these groups

Abstract

We define cohomological complexes of locally compact abelian groups associated with varieties over $p$-adic fields and prove a duality theorem under some assumption. Our duality takes the form of Pontryagin duality between locally compact motivic cohomology groups.