2015/05/21 by Carlos D'Andrea, Carlos D’Andrea, Alina Ostafe +7
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Coding theory and cryptography #Commutative Algebra (math.AC) #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT) #math.AC #math.DS #math.NT
paper · pdf · doi:10.48550/arxiv.1505.05814
openalex publication_date 2015/05/21 · arxiv created 2017/04/27 · arxiv updated 2017/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give bounds for the number and the size of the primes p such that a reduction modulo p of a system of multivariate polynomials over the integers with a finite number T of complex zeros, does not have exactly T zeros over the algebraic closure of the field with p elements. We apply these bounds to study the periodic points and the intersection of orbits of algebraic dynamical systems over finite fields. In particular, we establish some links between these problems and the uniform dynamical Mordell-Lang conjecture.