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AN UPPER BOUND FOR THE GENERALISED GREATEST COMMON DIVISOR OF RATIONAL POINTS

Part of: Arithmetic algebraic geometry Arithmetic problems. Diophantine geometry Elementary number theory

Published online by Cambridge University Press:  20 January 2025

BENJAMÍN BARRIOS Open the ORCID record for BENJAMÍN BARRIOS [Opens in a new window]
BENJAMÍN BARRIOS*
Affiliation:
Departamento de Matemáticas, Facultad de Matemáticas, Pontificia Universidad Católica de Chile, 4860 Av. Vicuña Mackenna, Macul, RM, Chile
*
e-mail: [email protected]
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Abstract

Let X be a smooth projective variety defined over a number field K. We give an upper bound for the generalised greatest common divisor of a point $x\in X$ with respect to an irreducible subvariety $Y\subseteq X$ also defined over K. To prove the result, we establish a rather uniform Riemann–Roch-type inequality.

Keywords

heightgreatest common divisorrational pointRiemann–Roch

MSC classification

Primary: 11G50: Heights
Secondary: 11A05: Multiplicative structure; Euclidean algorithm; greatest common divisors 14G05: Rational points
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , First View , pp. 1 - 6
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

Supported by ANID Master’s Fellowship Folio 22221062 from Chile.

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