Seminar | January 27 | 3-4:30 p.m. | 891 Evans Hall
Silvain Rideau, UC Berkeley
A result of Pillay's state that a group definable in a differentially closed field can be embedded in an algebraic group. Similar theorems have also been proved in various structures of enriched fields: separably closed fields, fields with a generic automorphism, real closed fields... Moreover, the proofs of all these results use similar tools developed to study groups in stable, and then simple, theories.
The goal of my talk will be to explain those results and some of the tools involved in proving them. Then, I will explain how, in certain cases, we can get rid of the stability assumptions in those proofs to use them in valued fields.