The inverse sieve problem for algebraic varieties over global fields

• Juan Manuel Menconi ^[2] ; Marcelo Paredes ^[1] ; Román Sasyk ^[2]
  1. [1] Universidad de Buenos Aires

     Universidad de Buenos Aires

     Argentina

     
  2. [2] Instituto Argentino de Matemática Alberto P. Calderón, Buenos Aires
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 37, Nº 6, 2021, págs. 2245-2284
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • Let K be a global field and let Z be a geometrically irreducible algebraic variety defined over K. We show that if a big set S⊆Z of rational points of bounded height occupies few residue classes modulo p for many prime ideals p, then a positive proportion of S must lie in the zero set of a polynomial of low degree that does not vanish at Z. This generalizes a result of Walsh who studied the case when S⊆{0,…,N}d.