Submission date: 26 April 2024

Abstract:

We prove generic differentiability in P-minimal theories, strengthening an earlier result of Kuijpers and Leenknegt. Using this, we prove Onshuus and Pillay's P-minimal analogue of Pillay's conjectures on o-minimal groups. Specifically, let G be an n-dimensional definable group in a highly saturated model M of a P-minimal theory. Then there is an open definable subgroup H ⊆ G such that H is compactly dominated by H/H^{00}, and H/H^{00} is a p-adic Lie group of the expected dimension.

Mathematics Subject Classification: 03C45, 03C60, 12L12

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Full text arXiv 2404.17234: pdf, ps.