Greatest common divisors of \(u-1, v-1\) in positive characteristic and rational points on curves over finite fields

DOI10.4171/JEMS/409zbMath1325.11060OpenAlexW2000693464MaRDI QIDQ363241

Umberto Zannier, Pietro Corvaja

Publication date: 2 September 2013

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/jems/409

zbMATH Keywords

Diophantine approximationcurves over finite fieldsVojta's conjecture

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Finite ground fields in algebraic geometry (14G15) Local ground fields in algebraic geometry (14G20) Varieties over finite and local fields (11G25)

Related Items (14)

Polynomial Equations in Subgroups and Applications ⋮ On some extensions of the Ailon-Rudnick theorem ⋮ Greatest common divisors of iterates of polynomials ⋮ Double character sums with intervals and arbitrary sets ⋮ Arithmetic and dynamics on varieties of Markoff type ⋮ Greatest common divisors for polynomials in almost units and applications to linear recurrence sequences ⋮ A variant of a theorem by Ailon-Rudnick for elliptic curves ⋮ The dynamical zeta function for commuting automorphisms of zero-dimensional groups ⋮ Markoff triples and strong approximation ⋮ Identity testing and interpolation from high powers of polynomials of large degree over finite fields ⋮ Generalized greatest common divisors for orbits under rational functions ⋮ Solutions of polynomial equations in subgroups of \(\mathbb{F}_p^*\) ⋮ Intersections in subvarieties of ${\mathbb {G}}_{\mathrm {m}}^l$ and applications to lacunary polynomials ⋮ A cyclotomic generalization of the sequence \(\gcd(a^n-1, b^n-1)\)

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