The inverse sieve problem for algebraic varieties over global fields

  • Juan Manuel Menconi

    Instituto Argentino de Matemática Alberto P. Calderón, Buenos Aires, and Universidad de Buenos Aires, Argentina
  • Marcelo Paredes

    Universidad de Buenos Aires, Argentina
  • Román Sasyk

    Instituto Argentino de Matemática Alberto P. Calderón, Buenos Aires, and Universidad de Buenos Aires, Argentina
The inverse sieve problem for algebraic varieties over global fields cover
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Abstract

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

Cite this article

Juan Manuel Menconi, Marcelo Paredes, Román Sasyk, The inverse sieve problem for algebraic varieties over global fields. Rev. Mat. Iberoam. 37 (2021), no. 6, pp. 2245–2284

DOI 10.4171/RMI/1261