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Seminar

DDC - Valuation Theory: Groups definable in difference-differential fields September 09, 2020 (09:00 AM PDT - 10:00 AM PDT)
Parent Program:
Location: SLMath: Online/Virtual
Speaker(s) Zoé Chatzidakis (École Normale Supérieure)
Description

Valuation theory plays a major part in the interaction between number theory and logic. In this seminar, a variety of topics from valuation theory, and in particular connections to model theory, will be discussed. There will be a strong emphasis on results involving the definability of valuations.

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

Groups Definable In Difference-Differential Fields

Abstract/Media

Valuation theory plays a major part in the interaction between number theory and logic. In this seminar, a variety of topics from valuation theory, and in particular connections to model theory, will be discussed. There will be a strong emphasis on results involving the definability of valuations.

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

 

In the context of a differentially closed field U of characteristic 0 with m commuting derivations (DCF_m) Phyllis Cassidy showed that if a group G is definable, contained in H(U), and Zariski dense in H where H is a simple algebraic group, then in fact G is conjugate to H(L), where L is "a field of constants".

With Bustamante and Montenegro, we generalize this to the context of DCF_mA, i.e., one adds a generic automorphism. The statement is a little different, since there are other fields around (Fix(\sigma) for instance), but similar. All definitions will be given, do not be scared by the apparently technical terms of the abstract.

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Groups Definable In Difference-Differential Fields

H.264 Video 25139_28637_8487_Groups_Definable_in_Difference-Differential_Fields.mp4