Cycle conjectures and birational invariants over finite fields
Algebraic Geometry
2025-12-23 v2 Number Theory
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.
Cite
@article{arxiv.2406.14438,
title = {Cycle conjectures and birational invariants over finite fields},
author = {Samet Balkan and Stefan Schreieder},
journal= {arXiv preprint arXiv:2406.14438},
year = {2025}
}
Comments
34 pages, final version, to appear in Selecta Mathematica