2022/10/21 by Xiaozong Wang, Wang, Xiaozong
Mathematics · Social Sciences · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #Vietnamese History and Culture Studies
paper · pdf · doi:10.48550/arxiv.2210.12013
openalex publication_date 2022/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let X be a smooth projective variety defined over a finite field. We show that any algebraic 1-cycle on X is rationally equivalent to a smooth 1-cycle, which is a ℤ-linear combination of smooth curves on X. We also prove a generalized version of Poonen's Bertini theorem over finite fields. Given a very ample line bundle L on X and an arbitrary line bundle M, this version implies the existence of a global section of M⊗ L⊗ d for sufficiently large d whose divisor is smooth.