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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: MSRI: Online/Virtual
Speaker(s) Sylvy Anscombe (Institut de Mathematiques de Jussieu)
Description

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

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

H.264 Video 25435_28993_8657_Diophantine_Subsets_and_Subfields_of_Large_Fields.mp4