To participate in this seminar, please register here: https://www.msri.org/seminars/25206

Abstract:

The class of large fields includes plenty of familiar examples: algebraically closed, separably closed, real closed, p-adically closed, pseudo algebraically closed, pseudo real closed, etc. In many cases,these fields can be understood model theoretically -- for example, by an axiomatisation of the complete theory, or even a quantifier elimination.

In his 2010 paper, Arno Fehm showed that any infinite diophantine subset of a perfect large field is not contained in any proper subfield. We will give a proof of an analogous result for imperfect large fields, and explore links with definability in henselian valued fields.

Diophantine Subsets And Subfields Of Large Fields