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

2025/01/20 by BENJAMÍN BARRIOS · 1 citation
Mathematics · Computer Science · #Mathematics and Applications #Polynomial and algebraic computation #Algebraic Geometry and Number Theory

paper · doi:10.1017/s0004972724001229

Abstract

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∈ X with respect to an irreducible subvariety Y⊆ X also defined over K . To prove the result, we establish a rather uniform Riemann–Roch-type inequality.

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• Growth of generalized greatest common divisors along orbits of self-rational maps on projective varieties

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