An upper bound for the generalized greatest common divisor of rational points

2024/11/09 by Barrios, Benjamín
Computer Science · Mathematics · #14G05 #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT) #Primary 11G50 #Secondary 11A05

paper · pdf · doi:10.48550/arxiv.2411.06050

openalex publication_date 2024/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X be a smooth projective variety defined over a number field K. We give an upper bound for the generalized 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 stablish a rather uniform Riemann--Roch type inequality.

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