Definable groups in henselian valued fields

Abstract: A valued field is henselian if every simple root of a polynomial in its residue field lifts uniquely to a root in the field itself. The Ax-Kochen-Ershov Principle states that henselian valued fields are—in the model-theoretic sense—determined by their value groups and residue fields, which are much simpler mathematical structures. This naturally leads to the question: Can every definable group in a henselian valued field be decomposed into components that are controlled by its value group and residue field? Hrushovski and Rideau-Kikuchi have answered this question positively for abelian groups in algebraically closed valued fields. In this talk, we will discuss our approach and results extending their work to the broader henselian setting. This is joint work with Paul Z. Wang.

logicnumber theory

Audience: researchers in the topic

Online logic seminar

Series comments: Description: Seminar on all areas of logic