2021/09/02 by Jordan S. Ellenberg, Ellenberg, Jordan S., Brian Lawrence +3 · 1 citation
Mathematics · Social Sciences · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #Vietnamese History and Culture Studies
paper · pdf · doi:10.48550/arxiv.2109.01043
openalex publication_date 2021/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let X be a quasi-projective variety over a number field, admitting (after passage to ℂ) a geometric variation of Hodge structure whose period mapping has zero-dimensional fibers. Then the integral points of X are sparse: the number of such points of height ≤ B grows slower than any positive power of B. For example, homogeneous integral polynomials in a fixed number of variables and degree, with discriminant divisible only by a fixed set of primes, are sparse when considered up to integral linear substitutions.