Generic differentiability and $P$-minimal groups
| Autor: | Johnson, Will |
|---|---|
| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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 $H \subseteq G$ such that $H$ is compactly dominated by $H/H^{00}$, and $H/H^{00}$ is a $p$-adic Lie group of the expected dimension. Additionally, the generic differentiability theorem immediately implies a classification of interpretable fields in $P$-minimal theories, by work of Halevi, Hasson, and Peterzil. Comment: 51 pages, this version adds Observation 8.6 on definable groups |
| Databáze: | arXiv |
| Externí odkaz: |
|