| Résume | This is a joint work with Ronald Bustamante Medina and Zoé
Chatzidakis.
In this talk we are interested in differential and difference fields
from the model-theoretic point of view. A differential field is a
field with a set of commuting derivations and a
difference-differential field is a differential field equipped with
an automorphism which commutes with the derivations.
Cassidy studied definable groups in differentially closed fields, in
particular she studied Zariski dense definable subgroups of simple
algebraic groups and showed that they are isomorphic to the rational
points of an algebraic group over some definable field. In this talk
we study groups definable in existentially closed
difference-differential fields. In particular, we study Zariski
dense definable subgroups of simple algebraic groups, and show an
analogue of Phyllis Cassidy's result for partial differential
fields. |
