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Seminar

DDC - Model Theory Seminar: Diophantine subsets and subfields of large fields November 30, 2020 (08:00 AM PST - 09:00 AM PST)
Parent Program:
Location: SLMath: Online/Virtual
Speaker(s) Sylvy Anscombe (Institut de Mathématiques de Jussieu–Paris Rive Gauche)
Description

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

Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

Diophantine Subsets And Subfields Of Large Fields
Abstract/Media

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.

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Diophantine Subsets And Subfields Of Large Fields

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