[en] We continue our earlier study of finite dimensional definable groups in
models of the the model companion of an o-minimal L-theory T expanded by a
generic derivation as in [F-K].
We generalize Buium's notion of an algebraic D-group to L-definable
D-groups, namely (G,s), where G is a L-definable group in a model of T, and s
is an L-definable group section into the prolongation of G. Our main theorem
says that every definable group of finite dimension in a model of the theory is
definably isomorphic to the ``sharp'' points of an L-definable D-group.
We obtain analogous results when T is either the theory of p-adically closed
fields or the theory of pseudo-finite fields of characteristic zero.
Disciplines :
Mathematics
Author, co-author :
Ya'acov Peterzil
Pillay, Anand
Point, Françoise ; Université de Mons - UMONS > Faculté des Science > Service de Logique mathématique
Language :
English
Title :
On definable groups and D-group in certain fields with a generic derivation
