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Uniform bounds for the
number of rational points on varieties over global fields
Marcelo Paredes and Román Sasyk |
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Vol. 16 (2022), No. 8, 1941–2000
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Abstract |
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We extend the work of Salberger; Walsh; Castryck, Cluckers, Dittmann and Nguyen; and Vermeulen to prove the uniform dimension growth conjecture of Heath-Brown and Serre for varieties of degree at least over global fields. As an intermediate step, we generalize the bounds of Bombieri and Pila to curves over global fields and in doing so we improve the factor by a factor. |
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Keywords
varieties over global fields, heights in global fields,
number of rational solutions of diophantine equations,
determinant method
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Mathematical Subject Classification
Primary: 11D45, 11G35, 11G50, 14G05
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Milestones
Received: 28 February 2021
Revised: 14 August 2021
Accepted: 12 November 2021
Published: 29 November 2022
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Authors |
| Marcelo Paredes | |
| Department of Mathematics Facultad de Ciencias Exactas y Naturales Universidad de Buenos Aires Ciudad Universitaria – Pabellón I 1428 Ciudad Autónoma de Buenos Aires Argentina |
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| Román Sasyk | |
| Department of Mathematics Facultad de Ciencias Exactas y Naturales Universidad de Buenos Aires Ciudad Universitaria – Pabellón I 1428 Ciudad Autónoma de Buenos Aires Argentina |
Instituto Argentino de Matemáticas
Alberto P. Calderón-CONICET Saavedra 15, Piso 3 1083 Ciudad Autónoma de Buenos Aires Argentina |
