Seminar
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Location: | SLMath: Online/Virtual |
To participate in this seminar, please register here: https://www.msri.org/seminars/25206
Diophantine Subsets And Subfields Of Large Fields
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
H.264 Video | 25435_28993_8657_Diophantine_Subsets_and_Subfields_of_Large_Fields.mp4 |