Cycle conjectures and birational invariants over finite fields

2024/06/20 by Samet Balkan, Stefan Schreieder, Balkan, Samet +1
Computer Science · Mathematics · #14C15 #14C25 #Algebraic Geometry (math.AG) #Coding theory and cryptography #Cryptography and Residue Arithmetic #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2406.14438

openalex publication_date 2024/06/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

We study a natural birational invariant for varieties over finite fields and show that its vanishing on projective space is equivalent to the Tate conjecture, the Beilinson conjecture, and the Grothendieck--Serre semi-simplicity conjecture for all smooth projective varieties over finite fields. We further show that the Tate, Beilinson, and 1-semi-simplicity conjecture in half of the degrees implies those conjectures in all degrees.

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