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

Published online by Cambridge University Press:  20 January 2025

BENJAMÍN BARRIOS*
Affiliation:
Departamento de Matemáticas, Facultad de Matemáticas, Pontificia Universidad Católica de Chile, 4860 Av. Vicuña Mackenna, Macul, RM, Chile

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.

Type
Research Article
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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