On definable groups and D-group in certain fields with a generic derivation
Logic
2023-05-29 v1
Abstract
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.
Cite
@article{arxiv.2305.16747,
title = {On definable groups and D-group in certain fields with a generic derivation},
author = {Ya'acov Peterzil and Anand Pillay and Francoise Point},
journal= {arXiv preprint arXiv:2305.16747},
year = {2023}
}