Residue field domination in some henselian valued fields

TL;DR

This paper extends the theory of stable and residue field domination to certain henselian valued fields with bounded Galois groups, offering new characterizations in algebraically closed valued fields.

Contribution

It generalizes previous results on stable domination to a broader class of henselian valued fields with bounded Galois groups and provides an alternative characterization in algebraically closed valued fields.

Findings

Extended stable domination results to henselian valued fields with bounded Galois group

Provided an alternative characterization of stable domination in algebraically closed valued fields

Broadened understanding of residue field domination in valued field theories

Abstract

We generalize previous results about stable domination and residue field domination to henselian valued fields of equicharacteristic 0 with bounded Galois group, and we provide an alternate characterization of stable domination in algebraically closed valued fields for types over parameters in the field sort.