On definable groups and D-group in certain fields with a generic derivation

Ya'acov Peterzil; Anand Pillay; Francoise Point

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arXiv · 2305.16747

On definable groups and D-group in certain fields with a generic derivation

Ya'acov Peterzil·Anand Pillay·Francoise Point

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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.

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BibTeX RIS

Ya'acov Peterzil, Anand Pillay, Francoise Point. 2023-05-26. On definable groups and D-group in certain fields with a generic derivation. https://arxiv.org/abs/2305.16747

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