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arXiv · 2406.14438

Cycle conjectures and birational invariants over finite fields

Samet Balkan·Stefan Schreieder
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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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Samet Balkan, Stefan Schreieder. 2024-06-20. Cycle conjectures and birational invariants over finite fields. https://arxiv.org/abs/2406.14438

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