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Uniform Yomdin–Gromov
parametrizations and points of bounded height in valued
fields
Raf Cluckers, Arthur Forey and François Loeser |
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Vol. 14 (2020), No. 6, 1423–1456
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Abstract |
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We prove a uniform version of non-Archimedean Yomdin–Gromov parametrizations in a definable context with algebraic Skolem functions in the residue field. The parametrization result allows us to bound the number of -points of bounded degrees of algebraic varieties, uniformly in the cardinality of the finite field and the degree, generalizing work by Sedunova for fixed . We also deduce a uniform non-Archimedean Pila–Wilkie theorem, generalizing work by Cluckers–Comte–Loeser. |
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Keywords
rational points, points of bounded height, parametrizations
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Mathematical Subject Classification 2010
Primary: 14G05
Secondary: 03C98, 11D88, 11G50
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Milestones
Received: 18 February 2019
Revised: 9 January 2020
Accepted: 3 March 2020
Published: 30 July 2020
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Authors |
| Raf Cluckers | |
| University of Lille CNRS, UMR 8524 – Laboratoire Paul Painlevé F-59000 Lille France |
KU Leuven Department of Mathematics Leuven Belgium |
| Arthur Forey | |
| D-Math ETH Zürich Zürich Switzerland |
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| François Loeser | |
| Institut Universitaire de
France Sorbonne Université UMR 7586 CNRS Institut Mathématique de Jussieu Paris France |
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