One dimensional commutative groups definable in algebraically closed valued fields and in the pseudo-local fields

TL;DR

This paper classifies one-dimensional definable groups in algebraically closed valued fields and pseudo-local fields, providing a comprehensive list up to finite modifications.

Contribution

It offers a complete classification of one-dimensional definable groups in these fields, extending understanding of their algebraic and model-theoretic structure.

Findings

Complete list of definable groups in the specified fields

Classification up to finite index and finite subgroup quotients

Enhanced understanding of group structures in valued fields

Abstract

We give a complete list of the one-dimensional groups definable in algebraically closed valued fields and i the pseudo-local fields, up to a finite index subgroup and a quotient by a finite subgroup.