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AN UPPER BOUND FOR THE GENERALISED GREATEST COMMON DIVISOR OF RATIONAL POINTS
Part of:
Arithmetic algebraic geometry
Elementary number theory
Arithmetic problems. Diophantine geometry
Published online by Cambridge University Press: 20 January 2025
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.
MSC classification
Primary:
11G50: Heights
- Type
- Research Article
- Information
- Copyright
- © The Author(s), 2025. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.
Footnotes
Supported by ANID Master’s Fellowship Folio 22221062 from Chile.
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