Seminar
Parent Program: | |
---|---|
Location: | SLMath: Online/Virtual |
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
Groups Definable In Difference-Differential Fields
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.
![]() |
Notes
|
Groups Definable In Difference-Differential Fields
H.264 Video | 25139_28637_8487_Groups_Definable_in_Difference-Differential_Fields.mp4 |